(written from a Production point of view)
Star Trek: Enterprise Edit
Star Trek Nemesis Edit
In Star Trek Nemesis, a trail of smoke briefly appeared behind the nacelles of the USS Enterprise-E when the ship accelerated to warp speed. The effect has not been used in any other Star Trek production. 
Star Trek Into Darkness Edit
Conceptually, the Enterprise's warp contrails were intended to be a new addition made to the ship between Star Trek and Star Trek Into Darkness. Regarding the addition of the contrails, Lindelof explained, "That was driven by a few things. One was to show the audience that Scotty has made modifications to the Enterprise between the two films [...] since Scotty is now the [chief] engineer." The filmmakers were mindful that, in adding the warp contrails, they didn't deviate from canon too much, such as if they had added a cloaking device to the Enterprise's systems instead. The warp contrails were depicted with CGI. Said Lindelof, "Roger Guyett, our visual effects supervisor, took J.J.'s phrase 'warp contrails' and ran with it [....] Roger tried a few tests, some of which felt a bit too radical, but it was basically us [...] saying 'wow, that looks cool.' And we went with it."