(written from a Production point of view)
The Stargate franchise is a series of science fiction television shows and films about a modern secret US Air Force unit exploring the galaxy through an interstellar network of ancient portals. The primary series, Stargate SG-1, had a 10 season run, longer than any individual Star Trek series, or, as of 2016, any other American science fiction series.
The franchise has made numerous references to Star Trek and has featured appearances by a number of actors who had previously appeared in various Star Trek series. In particular, Robert Picardo (the Doctor on Star Trek: Voyager) had a recurring role as Richard Woolsey beginning with the Stargate SG-1 episode "Heroes, Part 2". Woolsey later joined the main cast of Stargate Atlantis for its fifth and final season.
Like Battlestar Galactica, the ancient astronaut idea is central to the plot of the franchise, if not more so. The idea that the basis of human gods were originally powerful extraterrestrials was explored previously on Star Trek, as was the notion that various ancient cultures from Earth were exported to other planets. TNG also features a "Stargate" of its own.
Unlike Star Trek, Battlestar Galactica or Star Wars, actual space ships play a diminished role in the series and most travel between planets is done by a series of artificial Wormholes that give the series its name. The action is also set largely within the present day, rather than the future.
The original movie plays on the premise that the Ancient Egyptian civilization was created by aliens masquerading as gods, particularly a being called Ra, but that humans were able to expel them and close off the Stargate which led to Earth. By the time it was re-opened, humans had advanced by thousands of years.
The premise is somewhat similar to Who Mourns for Adonais? in TOS where the Enterprise encounters what appear to have been the models for Ancient Greek gods. These gods are more playful than Ra is in Stargate.
A third possible influence might be Star Trek V: The Final Frontier, which features the protagonists looking for the source of early history and having to fight a powerful being which has masqueraded as a number of gods.
Whenever Teal'c is out of the Stargate Command on Earth he wears a hat or headband to cover his head badge, just like Mr. Spock covers his ears when traveling to Earth's past or a primitive people.
"Children of the Gods"Edit
Arriving on Abydos, Major Ferretti gives Daniel Jackson a Vulcan hand salute.
This season 1 episode features Armin Shimerman in a major guest role.
This season 2 episode has Jack O'Neill identifying himself as "Captain James T. Kirk of the Starship Enterprise" when captured by the US Air Force, after traveling back in time.
"Point of View"Edit
In this episode, an alternate Carter and Kawalsky ask "our" SG-1 to save their world, located in a parallel universe, from the Goa'uld. O'Neill and Daniel go to the alternate "half-evil" universe, where Apophis and his First Prime, Teal'c, have goatees. In the normal universe, Teal'c is an ally to the main protagonists and Apophis, though an enemy, does not have a goatee. This is a reference to the TOS episode "Mirror, Mirror".(citation needed • edit)
When asked if he could "beam" Colonel O'Neill and Teal'c out from the X-301, Jacob Carter retorts, "What am I, Scotty?"
In the background of a shot, a tourist can be seen posing for a photograph while performing the Vulcan hand salute.
Cadet Hailey refers to zat'nik'tels as "those phaser things".
When Tanner and the others beam up to their ship at the end of the episode, the beam pattern and color is the same as that of the transporter beam from Star Trek: The Original Series.
"Redemption, Part 1"Edit
While Major Samantha Carter is performing a system's check on the prototype X-302 fighter-interceptor, she mentions inertial dampers. Colonel Jack O'Neill then asks for the report on phasers, in which Carter denies his request to his disappointment.
"The Other Guys"Edit
Dialogue in the episode includes:
- Felger: "Bite me, Coombs! At least my heroes exist! If this was a Trek convention, you'd be all dressed up like a Klingon!"
- Coombs: "Vulcan, Felger, Vulcan! And I don't know how you can call yourself a scientist and not worship at the altar of Roddenberry!"
- Coombs: "Oh, come on, Felger. We might as well be wearing red shirts!"
There was also a bat'leth visible above Lord Khonsu's throne.
This season 6 episode features an exchange between Carter and O'Neill about the name of the first Earth spaceship:
- O'Neill: "They didn't go for it."
- Carter: "They didn't approve the mission?"
- O'Neill: "Well no, they did that. Once they knew the stakes and the whole fate of the universe stuff, both the President and Hammond realized we had no choice. They wish us luck, God speed and all those things he says when he thinks we're gonna die."
- Carter: "So what didn't they go for?"
- O'Neill: "The name I suggested."
- Carter: "For the ship?"
- O'Neill: "Yeah."
- Carter: "Ah, sir... we can't call it the Enterprise."
- O'Neill: "Why not?"
"Evolution Part I"Edit
When Colonel O'Neill and company are taken prisoner by a Goa'uld, a Jaffa approaches them. O'Neill says, "Greetings," and makes a half-hearted Vulcan salute.
Colonel Mitchell concludes that members of SG-1 from an alternate universe aren't evil because they don't have beards.
In the final moments of this episode, the main characters of Teal'c, Vala, Carter, and Mitchell are seen playing poker and the episode ends with General Landry joining in the game. This is very similar to the series finale of Star Trek: The Next Generation, when Picard joins in on the senior staff poker game.
The 200th episode of Stargate SG-1 was planned as an homage to its many fans. It had many different references to other shows, and included one to Star Trek: The Original Series.
While pitching movie ideas to the crew of SG-1, Martin Lloyd – the person from the studio – comes up with a brilliant idea. He begins to describe it and the scene shifts to the bridge of a Daedalus-class ship (as shown in the Stargate Universe). Mitchell is wearing command division red while acting like Kirk. Carter is shown wearing an earpiece like Uhura's. Teal'c is shown acting like Worf at a security station. Daniel is shown looking into a science monitor like Spock often did (and acting like McCoy). The episode even shows a Scottish engineer in the ship's engine room. Back in reality, Daniel spots the ripoff.
In a few episodes, Dr. Carson Beckett objects to physical labor by starting a sentence "I'm a doctor, not a..." similar to Dr. McCoy. In one episode, John Sheppard mentions Dr. McCoy, then explains, "That's the person Dr. Beckett plays in real life," after realizing that residents of another galaxy didn't understand the reference.
Dr. Carson Beckett says to Sheppard, "I hear you got yourself a cling-on."
"The Defiant One"Edit
This is the first episode in which Rodney McKay describes John Sheppard as being similar to Captain Kirk. When a hostile alien known as the Wraith takes over his spaceship known as a Puddle Jumper, Rodney says "What are you? Captain Kirk?"
Rodney McKay often describes John Sheppard as being similar to Captain James T. Kirk; on a planet the team visits, Sheppard is able to score a romantic scene with a beautiful alien woman.
The team finds an ancient ship where Colonel Sheppard tells Dr. McKay that they cannot call the ship the Enterprise. They instead call it the Orion, at Sheppard's insistence.
"McKay and Mrs. Miller"Edit
Rodney McKay calls Sheppard "Kirk" after Sheppard introduces himself to McKay's sister, Jeannie Miller.
A member of the Atlantis crew talks with a co-worker and complains about the fact that Rodney McKay never remembers his name, or uses a false name for him. He said that when McKay ever does it again, he will call him "McCoy" instead of "McKay", a reference to Leonard McCoy.
The Atlantis expedition crew adopt a Star Trek-like uniform color code among the civilian staff, with the expedition leaders (Weir, Carter, and Woolsey, the latter of whom was played by Robert Picardo) wearing red and scientists wearing blue. Several references were made since Picardo's addition to the cast in the show's final season.
In the episode "Vegas", Rodney McKay makes a remark about a Wraith getting a job as a Klingon at Star Trek: The Experience, but Woolsey (played by Robert Picardo) tells him that it's been shut down and Radek Zelenka was disappointed by the news telling them both that he wanted to see it.
Upon being suggested that Eli should tell his mother the truth, he says she can barely follow an episode of Star Trek.
Upon encountering a planet that's not in Destiny's database, and later revealed to be created artificially, Eli references the Genesis Device.
When Camile Wray complains that there aren't enough seats on Destiny's bridge, Colonel Young offers her his seat with all of the ship's controls on it. She refuses, saying it's his chair. He says "What am I, Captain Kirk? Sit in the chair."
February 2018 saw a revival attempt of the Stargate franchise with the launch of the ten-episode, ten-minute Origins webisode series on the occasion of its 20th anniversary, in which the existing mythology of the franchise is further expanded upon. The low-budget production features Star Trek: Enterprise star Connor Trinneer as one of the main characters.
Background information Edit
Long time Senior Illustrator Rick Sternbach, one of the most prolific production illustrators on the Star Trek live-action franchise, has stated on several occasions that he is an avowed fan of the Stargate franchise, remarking, "I’m a huge Stargate fanatic. Aside from the fact that a lot of our guys ended up on their show, including Bob Picardo, aside from that, they do Star Trek very well. I don’t mean that in a snarky way. They learned, they understood what makes a fun, semi-serious, science fiction show. There were a number of very forgettable space science fictions shows and films, like, Space Ranger, I think it was. You’ve got all the standard elements, space ships, astronauts, aliens, and for some reason they didn’t click. What they did with the Stargate concept was brilliant. The idea of a gateway to another star system is as old as science fiction, but what they did with the idea was tremendous." 
As far as science fiction is concerned, Stargate, has as of 2016 been in format, popularity and longevity, the third most successful franchise in American media history, after Star Trek and Star Wars. However, when counting the British produced Doctor Who franchise, it has been the fourth for longevity, Doctor Who actually being the oldest of them all and still up and running. Despite attaining a cult status, after live-action production had been suspended in 2011, interest in Stargate as a franchise, waned sharply and quickly, and while considerable, its longevity has not come anywhere near that of Star Trek, or Star Wars for that matter.