Some of my saddest moments from Trek (although many have been said before):
TOS
When Spock says it was the only time he was ever happy in This Side of Paradise
When Kirk loses Miramanee at the Obelisk
TOS Movies
Spock's death and funeral was the first time I ever cried at a movie (I still love that version of Amazing Grace!)
TNG
The Inner Light, possibly the best TNG episode, the flute playing at the end is so sad
The Relic, my 2nd favorite, Scotty on the holodeck Enterprise, no bloody A, B, C or D!
Star Trek (2009)
The Kelvin sequence, it was so sad watching George Kirk, sacrificing himself and knowing he will never see his family
I know some will disagree, but that scene is destined to be a classic Trek moment in the same category as Spock's death scene.