Recently I've unlocked the geek achievement of having watched all the Star Trek films. Here's a round up of all twelve--which ones are classics, and which ones you should avoid like The Borg.
Note: the number in brackets is my ranking.
The Original Series
Star Trek: The Motion Picture, Robert Wise, 1979 
Several years after the end of the television series, the now Admiral Kirk takes command of a newly refurbished Enterprise and goes after a mysterious entity known as V'ger that's threatening the planet. Not quite as awful as its reputation suggests. If you stripped away all the extraneous special effects (which do look great), you'd have a perfectly workable episode of the TV series... about 50 minutes out of a 2+ hour movie.
Star Trek II: The Wrath of Khan, Nicholas Meyer, 1982 
The second instalment of the movie franchise sees the return of a villain from the TV show's first season, the super-human Khan, who's hell bent on revenge. Kirk and crew have to stop him from using the Genesis Device, a life-creating machine invented by the ex-Mrs. Kirk and her son, as a weapon of mass destruction. Not only is the plot more focused than in TMP, but Kirk finally has to face up to the consequences of some of the total ass-pull moves he made earlier in his career, consequences that have deadly results for his closest friend. Said death is the most poignant and tear-jerking in all of Star Trek.
Star Trek III: The Search for Spock, Leonard Nimoy, 1984 
My attempts to avoid spoilers in the previous synopsis have clearly failed. Spock is still out there somewhere, so Kirk et al steal the Enterprise to go find him. Although it does bring Spock back in a satisfactory manner, the film suffers from a lower budget and Nimoy's first-time direction.
Star Trek IV: The Voyage Home, Leonard Nimoy, 1986 
On their way back to face court-martial for stealing (and subsequently blowing up) the Enterprise, Kirk and crew find the Earth being threatened by some space whales, so naturally they have to travel back in time to present-day Earth to rescue a pair of humpbacks. Yep. While not quite as charming as, say, "The Trouble with Tribbles", TVH manages to capture the campy fun of the 60s series.
Star Trek V: The Final Frontier, William Shatner, 1989 
Spock's illogical half-brother steals the Enterprise to go look for God. Apart from some nice character moments (and so much Ho Yay!), this is pretty awful. Whose idea was it to let Shatner direct?
Star Trek VI: The Undiscovered Country, Nicholas Meyer, 1991 
On the eve of the Klingon's entry into the Federation, Kirk and McCoy are accused of assassinating their High Chancellor, and the crew must prove them innocent. Better direction, better effects (featuring impressive morphs from a shape-shifting Iman), and a solid story, TUC is easily one of the best in the Star Trek film franchise.
The Next Generation
Star Trek: Generations, David Carson, 1994 
Captain Picard teams up with the thought-to-be long-dead Captain Kirk to defeat this guy who's destroying planets basically just so he can go to his happy place. While the story wouldn't have made a bad episode of TNG, the addition of Kirk was unnecessary, making his death even more pointless than Lt. Yar's.
Star Trek: First Contact, Jonathan Frakes, 1996 
The Enterprise-E (yes, they blew it up again) travels back in time to thwart the Borg Collective's plan to stop humans from achieving warp speed. Lots of action, good effects, a bit of humour, and plenty of suspense. It's a really clever way to let us see the most important moment in Star Trek's backstory.
Star Trek: Insurrection, Jonathan Frakes, 1998 
Picard and crew go rogue to stop a Federation plot to meddle in the affairs of a peaceful planet. An intersting concept that plays out fairly well, though the silly campy moments aren't handled as well as in TVH.
Star Trek: Nemesis, Stuart Baird, 2002 
The Romulan clone of Captain Picard seeks revenge on his creators, the Federation, and the Captain himself. Again, an interesting concept that's entertaining, but I didn't like it because they killed off my all-time favourite Star Trek character for real and didn't even give him a funeral.
Star Trek, J. J. Abrams, 2009 
Young Jim Kirk and co. have to stop a vengeful Romulan who's traveled back from the future and messed up the timelines. Wonderful nods to TOS, great performances (especially from Zachary Quinto as he explores Spock's contradictory half-human half-Vulcan nature), and a perfect way to reboot the franchise while keeping everything from the originals canon.
Star Trek: Into Darkness, J. J. Abrams, 2013 
Kirk and the Enterprise crew must stop Benedict Khanberbatch from wrecking destruction across the galaxay. References to TOS seem a bit more forced this time around, plus it continues to draw out the 'how Kirk became Kirk' angle instead of just letting him be Captain Kirk. Really, it's just a shoddy remake of Wrath of Khan.