Here's something extremely nerdy to ponder while you enjoy whatever snack you're having for elevenses, a video compilation of "going to warp" scenes from all the pre-J.J. Abrams Star Trek movies, from 1979's Star Trek: The Motion Picture to Star Trek: Nemesis in 2002. (I saw a similar montage a couple days ago that included the 2009 reboot flick, but it seems to have vanished. My guess is some copyright nazi got wind of it. Clips from all those old movies? No problem. But don't go posting so much as five seconds of our shiny new Star Trek, you damn Internet bootlegging fanboys!)
Anyhow, it's interesting to me that the effect actually became less spectacular over time. You'd think the opposite would be the case as visual effects technology advanced and this stuff (presumably) became easier to create. Of course, the Trek movies did see their budgets whittled away over time, so that may have been a factor. In any event, I give you... Warp Speed!
Since all Trekkies have a genetic imperative to offer unsolicited opinions on meaningless stuff, I'd like to announce for the record that my favorite warp effects are the "disco-tunnel" from The Motion Picture and the Wrath of Kahn "rainbow streak." The TMP effect is the most spectacular of all of them, the most cinematic. The sound effects and the slightly drawn-out timing impart a sense of drama, as if massive energies are being harnessed and something truly extraordinary is about to happen. And of course, if you consider the historical context of this being the first time we'd seen the Enterprise on the big screen, and the desire (at that time) to make a Star Trek that really was something more than just a two-hour television segment, that's exactly what the jump to warp speed was supposed to be.
The Kahn effect (seen at 0:17 and 0:22, if you don't recognize them all on sight) wasn't as spectacular or as "big" -- I suspect it was cheaper to produce -- but it was impressive in its own right, and probably better for story-telling purposes, since it could be placed in context with other objects and backgrounds. (I can't quite imagine the TMP tunnel effect against the Mutara Nebula, the backdrop in the second Kahn clip; it seems as if it would only work if the Enterprise were alone in the frame.) Some variant of the rainbow streak would, of course, appear in all the rest of the movies derived from the original series, but for my money it was never as nicely done as in its first appearance.
As for the effect seen in the Next Generation movies, I was never a fan of the "rubberband" effect introduced in the Next Gen TV series, i.e., the way the ship seems to stretch out, then snap forward into the starburst/sonic boom thing. It always looked cheap and silly to me, and the big-screen version didn't improve upon it...