(covers information from several alternate timelines)
Speed limits were imposed by certain authorities in the Milky Way Galaxy, limiting the speed of vehicles, which included the warp factor at which starships were allowed to travel in their territories. The intentions of speed limits were often for safety concerns, such as minimizing the cumulative destructive effect of subspace emissions to the interstellar environment by warp-capable vessels.
In the 2240s of the alternate reality, an Iowa police officer used his hovercruiser to pursue a Corvette being driven by a young James T. Kirk, who was driving well over the posted speed limit. (Star Trek)
In the late-2360s, Hekaran scientists presented preliminary research to the Federation Science Council for evaluation, which alleged that warp fields were slowly damaging their region of space and that their homeworld Hekaras II would one day be rendered uninhabitable if nothing was done to prevent the damage being caused. The evidence didn't hold up at that point. (TNG: "Force of Nature")
In 2369, unusual energy readings of elevated thoron emissions in the plasma field were detected in the Denorios belt. They were speculated to be the environmental byproduct of the increased traffic and presence of many warp and impulse engines in the area. The effect appeared to be the formation of a subspace rupture. It was however discovered that the rupture was a manifestation of what Jadzia Dax imagined it to be, caused by aliens from the Gamma Quadrant. The elevated emissions turned out to be harmless. (DS9: "If Wishes Were Horses")
In 2370, the Hekaran scientist Serova opened a subspace rift by overloading her ships engines to a warp core breach in the Hekaran sector, demonstrating that conventional warp engines did in fact cause severe damage to the fabric of spacetime. In order to slow the rate of the damage, the Federation Council shared the findings with all known warp-capable species and imposed a speed restriction of warp factor 5 on all Federation vessels in all but extreme emergencies. The areas of space most damaged by that point were restricted to essential travel only. The Klingons were expected to follow the restrictions, but Deanna Troi and Worf thought it unlikely that the Romulans, the Ferengi and the Cardassians would. (TNG: "Force of Nature")
Later that year, the USS Enterprise-D was authorized by Admiral Margaret Blackwell to exceed warp speed limitations during the assignment to salvage the USS Pegasus. (TNG: "The Pegasus"). They were also given permission to exceed warp speed limitations when delivering urgently needed medical supplies to Barson II. (TNG: "Eye of the Beholder").
In 2378, The Doctor, disguised as Kathryn Janeway, informed the crew that hostile ecological extremist aliens had completely outlawed conventional warp drive inside their territory. They supposedly also believed all conventional warp drives cause damage to subspace, and had ordered the warp core of the USS Voyager to be ejected. The Doctor also referred to a fictional type of warp drive, supposedly decades ahead of Federation technology, called transphasic warp drive that didn't cause the damage. (VOY: "Renaissance Man")
- In Captains' Logs: The Unauthorized Complete Trek Voyages, page 294, Brannon Braga noted that in his opinion "when you limit warp drive, the rug is being pulled out from under Star Trek." And, according to Star Trek Encyclopedia (2nd ed., p. 187), since starships used speeds above warp 5 after 2370, a solution was presumably found to the problem, even though it was not mentioned on-screen.
- According to the Star Trek: Voyager series bible, Voyager could exceed the warp speed limit without polluting the space continuum due to its improved warp drive system.
- According to the unpublished VOY Season 1 edition of the Star Trek: Voyager Technical Guide, by Rick Sternbach and Michael Okuda, it is suggested that because of the variable geometry pylons used on Voyager, the generated warp fields might no longer have a negative impact on habitable worlds as established in "Force of Nature".