(written from a Production point of view)
Even in the series' first season, many story pitches ended up being unused for Enterprise. Fred Dekker, who worked on that initial season, later recalled, "On Enterprise, we staff writers would hear pitches a few times a month, and I came across a couple of ideas that I thought would make terrific episodes. So I would write these up and submit them thinking, 'Yeah, this is going to make for a great episode of Enterprise,' only to never hear anything about them again. It was like throwing ideas into a black hole." (Star Trek Magazine issue 180, p. 70)
Either late in ENT Season 2 or during the interim between that season and the next, Judith and Garfield Reeves-Stevens suggested multiple narrative ideas to Mike Sussman and Phyllis Strong. "We had a great meeting with Mike and Phyllis, and pitched all sorts of stories," remembered Garfield Reeves-Stevens. However, the plot concepts were deemed unnecessary because the series was about to enter a season-long arc exploring the Xindi incident and therefore didn't require a lot of standalone episodes. ("Before Her Time: Decommissioning Enterprise, Part One: New Voices", ENT Season 4 Blu-ray special features)
Undeveloped episodes during the run of the series
Tom Bergeron story
Billiard ball story
Sometime prior to the third season, Executive Story Editor André Bormanis pitched, to series co-creator and Executive Producer Brannon Braga, the concept of Enterprise encountering "a completely featureless planet, something that's the size of the Earth but is as smooth as a billiard ball," in Bormanis' words. Though he reckoned this was "a cool idea", he was unsure what the rest of the story should be about. Braga liked the notion of a featureless planet but asked Bormanis, "What's the story?" Years thereafter, Co-Executive Producer Chris Black commented, "I don't think we ever did the billiard ball in space." Bormanis agreed but felt a similar concept ended up being the Delphic Expanse spheres portrayed in the third season. ("Countdown" audio commentary, ENT Season 3 Blu-ray special features)
Boomers were originally to have featured more in the series' first season than they ultimately were; this was changed following the airing of the season's only Boomer-centric episode, "Fortunate Son". "We had another story or two planned with the Boomers," recalled Brannon Braga, "but we decided not to delve too much into meeting Humans all the time." Reasons for this were that the writers wanted to avoid making it seem as if Enterprise was close to Earth and preferred to focus on other aspects of the Travis Mayweather character than his heritage as a Boomer. (Star Trek: Communicator issue 139, p. 24)
Colonel Green story
During the fourth season, Manny Coto wanted to do a story featuring Colonel Green (with Peter Weller as Green). ("Terra Prime" audio commentary) Garfield and Judith Reeves-Stevens devised a story which was not only about Colonel Green but additionally concerned the NX class Columbia as well as the opening of the first starbase, which was designated Starbase 1. The Reeves-Stevenses also used the narrative to refer to a political movement called "the Optimum", which the writers reused from their novel Federation; the organization was linked to Colonel Green. The story additionally involved Malcolm Reed, establishing a heretofore secret connection between his great-grandfather and Colonel Green. "We had Malcolm crawling over the outside of the ship," commented Judith Reeves-Stevens. "It was wonderful."
The Reeves-Stevenses took the story idea to Manny Coto. "We'd worked it all out in our office, on cards, and we went in there," continued Judith Reeves-Stevens, "and I wish we'd had video of us doing this incredible presentation, where we were smacking those cards on, one after another, so Manny was so excited and said, 'I can't wait to do this episode.'" Garfield Reeves-Stevens added, "And so, Manny said, 'Yeah, I love this story. Write the outline.' So, we did an entire beat outline, took it to Manny, [he] said, 'Yes, this is great,' and Brannon [Braga] took one look at it and said, 'It's too dark.'" ("Observer Effect" audio commentary, ENT Season 4 Blu-ray special features)
Ultimately, the story was also not accepted because, in the words of Judith Reeves-Stevens, "Its lunch was eaten by the Soong," or, in other words, it became hard to do another story featuring genetically engineered Humans. (The Augment trilogy was actually conceived with Green as their leader, but the character was instead made an ancestor of Noonien Soong, to accommodate the fact that Brent Spiner was interested in appearing on the show.) Green (and Peter Weller) later featured in "Demons". ("Terra Prime" audio commentary)
One detail that would have featured in the undeveloped episode was a flag that had first appeared on a World War III uniform which the character of Q briefly wears in the pilot episode of Star Trek: The Next Generation, "Encounter at Farpoint"; in the Enterprise story, the flag would have been tied to Green's faction. A flag featuring the emblem was produced for the ENT episode "In a Mirror, Darkly", with the hope that it could be reused, but this never came to pass. 
A story idea involving the Klingon character of Korath, from Star Trek: Voyager series finale "Endgame", was thought up and pitched by the actor who played him, Star Trek veteran Vaughn Armstrong, who also portrayed Admiral Maxwell Forrest in Star Trek: Enterprise. (Star Trek: The Magazine Volume 2, Issue 9, p. 44; ) Armstrong stated, "An episode I would love to see would show Korath taking the time machine that Janeway stole from him and going back to stop Admiral Forrest from sending people out into space!" (Star Trek: The Magazine Volume 2, Issue 9, p. 44) Armstrong imagined Korath seizing the time machine from Janeway herself, and it was Forrest approving the launch of Enterprise NX-01, depicted in ENT pilot episode "Broken Bow", that the Klingon was attempting to prevent. "I'm plugging that because the overtime would be great," noted Armstrong. Although the make-up time would have also been extreme, Armstrong didn't find that a problem, feeling that the durations he spent in the make-up chair often allowed him time to memorize his lines. 
Mars independence story
During the fourth season, Manny Coto wanted to make an episode dealing with the Fundamental Declarations of the Martian colonies. The audio commentary for "Terra Prime" described it as a sort of Cuban Missile Crisis on Mars, with the comets used for terraforming the planet being aimed at Earth. The story never materialized, but the idea of comets being used for terraforming Mars found its way into "Demons".
Jack Treviño, Steve Fratt and Dr. Joseph DiLella pitched several Enterprise stories, all serving what Treviño described as "lesser utilized characters" (i.e., Phlox, Hoshi Sato, Travis Mayweather and Malcolm Reed). One of these stories involved Phlox being compelled, by a powerful force, to create Frankenstein-type creatures out of six different species, including Humans.
In the special features for the ENT Season 4 DVD, André Bormanis claimed that many ideas for Porthos episodes were pitched. These included Porthos becoming intelligent, Porthos being the only member of the crew capable of communicating with a canine alien, and even Porthos having to take command of the ship. Bormanis suggested that part of the reasoning why these stories weren't made was that the production staff didn't want Porthos stealing the show. Given the generally humorous tone of the segment, it might be that Bormanis was merely making these pitches up.
In addition, Breezy's handler claimed, in the segment, that he had suggested a story in which Porthos changes sex in a transporter accident, so to explain why the male Porthos was played by a female dog.
Pulp Fiction-like story
According to Linda Park in Star Trek: Communicator issue 147), Connor Trinneer pitched a story similar to Pulp Fiction, told from the perspective of aliens. The Enterprise NX-01 crew would speak gibberish until they found a way to communicate.
William Shatner two-parter
During the fourth season, there were efforts to write an episode that included a role for William Shatner. (Inside the Mirror Episodes, ENT Season 4 DVD special features) Scott Bakula endorsed the idea, excited at the idea of 'Kirk and Archer knocking heads.' (Star Trek Magazine issue 176, p. 64)
One of these early concepts involved the mirror universe. At the Grand Slam XIII Star Trek convention in March 2005, Manny Coto recalled, "We had talked about doing a mirror universe episode ever since we got into Season 4. But then we had the possibility of getting William Shatner. Coincidentally, the Reeves-Stevens [Judith and Garfield Reeves-Stevens, who had worked with Shatner on several Star Trek novels] were a pair of writers whom I desperately wanted to bring on the show. And they, it turned out, had an idea for a mirror universe two-parter which would feature the return of William Shatner."
At the same convention, Garfield Reeves-Stevens explained, "The idea was that the Tantalus field was not a disintegrator, it was a humane way of dealing with prisoners, by sending them back in time to a sealed penal colony. Enterprise (NX-01) comes upon the colony – and Tiberius [mirror-Kirk] is there. Tiberius thinks, 'Finally, a ship with a transporter – I can get back to my own universe, my own time.' He basically goes on the NX-01, gets to the transporter, sets it to go back to the mirror universe – the mirror universe doesn't exist." "It hasn't been created yet," Judith Reeves-Stevens added. Garfield continued, "So Tiberius and Archer work together to figure out where the division point is between the universes, what point that one split off into the other. And as it turns out, Tiberius and Archer together are responsible for the creation of the mirror universe."
William Shatner himself pitched this story concept to Executive Producers Manny Coto, Brannon Braga and Rick Berman, over lunch. The idea was well received by Coto, Berman and Braga. However, Berman pitched an alternative concept developed in-house by Producer Mike Sussman. The story, inspired by The Prisoner of Zenda and Akira Kurosawa's Kagemusha, would have seen Shatner playing Enterprise's heretofore unseen Chef, who would be revealed to be an ancestor of James T. Kirk. In Sussman's proposed story, Shatner's Chef and Captain Archer would be transported to the 23rd century by Daniels on a mission to preserve the timeline after Captain Kirk was kidnapped by temporal agents. Chef, with Archer's help, would be forced to impersonate his legendary descendant during an important historical event. Perhaps unsurprisingly, Shatner preferred the idea he had developed with the Reeves-Stevens. As Shatner and Paramount were unable to reach an agreement, the plans to have him included in the series were discarded. However, the desire to visit the mirror universe remained, and resulted in the production of "In a Mirror, Darkly" and "In a Mirror, Darkly, Part II".
In a memo Mike Sussman wrote Manny Coto (dated 20 August 2004), he suggested that, if they were unable to arrange a deal with William Shatner, they could perhaps do an episode or two with Leonard Nimoy playing Spock. Sussman proposed that the story, intended for the show's fourth season, might be based on a two-parter in The Young Indiana Jones Chronicles called "Mystery of the Blues", in which Harrison Ford guest starred as a middle-aged Indiana Jones in a framing story about how he learned to play jazz as a young man (with Sean Patrick Flanery playing the young version of the character).
As the memo continued, Sussman commented, "We could find Spock in the 24th century, a distinguished and retired Ambassador, who has a young visitor. Maybe this guy is a Vulcan/Human hybrid like Spock, and needs advice on balancing his two alien halves. This visit could lead Spock into recounting an adventure he had early in his career as a Starfleet cadet. This adventure could involve Young Spock (played by another actor) helping a middle-aged T'Pol (now in her early to mid-100's) on some vitally important mission…. In the process, Spock could learn some lesson which helped him choose his own path in life. We may learn a lot of new info on Spock…. Perhaps he was torn between life as a diplomat (like his father) and a career in Starfleet when he was a young man. The flashback adventure should involve Captain Archer (and other members of our cast) in old-age make-up, playing early 23rd century versions of themselves. Maybe their adventure is something of a 'Last Round-Up' for the old crew, whom T'Pol reunites for a secret and possibly illegal TBD mission. I thought it might be fun if our crew have to steal an antiquated NX-class ship from the Starfleet museum for one last adventure together." 
Tan Ru story
The stories which Jack Treviño, Steve Fratt and Dr. Joseph DiLella pitched included one involving Tan Ru, a probe that went on to, as established in TOS: "The Changeling", collide and merge with Nomad. According to Treviño, at the time Enterprise was canceled, there was every indication that this story was about to be sold.
Judith and Garfield Reeves-Stevens proposed a story where the NX-01 crew encountered members of the Trill species. Garfield Reeves-Stevens commented, "The idea being what would Archer’s reaction to the Trill be? We thought that to [the] first Humans to meet a joined species like the Trill […] would be something of a horror. It would be like a planet where the body snatchers had won." Judith Reeves-Stevens added, "And the Humans would want to separate them." The writers could not find a way to make their story work with DS9/TNG continuity. 
As part of an overview of the impact of Enterprise on the franchise, Star Trek Magazine reported that Linda Park had hoped to do a musical episode, to showcase the singing voices of John Billingsley and Scott Bakula, and her own ballroom dancing training. (Star Trek Magazine issue 176, p. 63)
Proposed fifth season episodes
As Star Trek: Enterprise was officially canceled on 2 February 2005, its fifth season was never produced. The series' producers, however, had already devised plans for future seasons, which could have begun to air by September 2005. (Most of this information is based on comments by Producer Manny Coto.)
At the 2009 VegasCon, Coto suggested that two story arcs in the fifth season would have been to show "origins of the Federation" and "whispers of the Romulan war". Consequently, the Romulans would be the major villains of the season, although other species may have appeared in the mini-arcs. 
Brannon Braga also noted that he and Rick Berman had considered making "Future Guy" a Romulan. . However, later, Braga claimed this was a red herring and that the season would have seen Future Guy revealed as Archer himself, trying to influence his younger self to set right the timeline.  
Manny Coto had also hoped that Season 5 would see more stories offering social commentary, compared to Season 4. 
Enterprise was due to revisit (or actually pre-visit) the cloud city Stratos on Ardana. In 2004, Manny Coto admitted, "I do want to do one or two episodes that take place on the Cloud City of Stratos. I want to see the early stages of that. I think it's a very fertile place for a storyline." (Star Trek Magazine issue 118, p. 23) Despite some initial ambivalence over whether he wanted the story to be comprised of one or two episodes, Manny Coto was later clearer about his intentions for the narrative's length when, in 2005, he spoke about how he regretted having been unable to fit the Stratos storyline into the fourth season. "I really wanted to do a two-parter on that location, to see Stratos in its earlier stages," he stated. "That was a wonderful location and wonderful setting for a great two-parter."
A Kzinti episode had been suggested which would have served as a prequel to TAS: "The Slaver Weapon". The concept progressed as far as a "rough rendering" of a Kzinti starship which writer Jimmy Diggs commissioned. The story was provisionally titled "Kilkenny Cats."  Manny Coto has stated that "Kilkenny Cats" was not an episode that they were developing "in any way, shape, or form." 
Mirror universe story
Revisits to the mirror universe and Hoshi Sato, now Empress of the Terran Empire, had also been discussed. At the 2009 VegasCon, Coto revealed that one idea was to spread four or five episodes through the season, as a kind of "mini-series inside a series." He said that it was his "big regret" that he had not managed to follow through on the idea. 
Brannon Braga revealed, via his Twitter account, that, before cancellation, there had been some talk about setting the entire fifth season in the mirror universe. 
Borg Queen origin story
Writer/producer Mike Sussman hoped to have T'Pol finally meet her father, and reveal to the audience that he was, in fact, a Romulan agent who had posed as a Vulcan officer prior to faking his own death. The suggestion that T'Pol was half-Romulan would have shed light on her affinity for Humans as well as her interest in experimenting with emotions. (, Information provided by Mike Sussman)
According to Entertainment Weekly, there was an episode "on the drawing board" to reportedly have featured Flint, under a previous alias, coming into contact with the crew of Enterprise. The episode never made it to a script write, but initial storyboard ideas suggested a confirmation of Flint's alias of Abramson as a famous Earth scientist with possible connections to Flint knowing either (or both) Henry Archer and Zefram Cochrane. The episode would have ended with some type of discovery of Flint's nature by Phlox, leading to Flint's negative views on discussing his background with anyone, thus avoiding the "disaster of intervention" that he mentioned later in the TOS episode.
In a 2009 interview, British writer/producer Russell T. Davies, showrunner of the British series Doctor Who, said that he had considered proposing a crossover between Doctor Who and Star Trek, but that the latter was canceled before the idea could be pursued.