Star Trek: Strategic Operations Simulator (Atari 8-bit computer - 1200xl if I recall correctly)
Star Trek: The Kobayashi Alternative (PC, DOS - first game I ever played on an IBM compatible, and still one of the best Trek games)
Star Trek: The Role Playing Game (Tabletop RPG. Gotten from a garage sale, not sure if it was complete. I did not play this except one time with a couple of my cousins and I'm pretty sure we didn't play it right. I really only used the book art as a basis to draw stuff - mostly ships, both shown in the book and loosely based on those.)
Star Fleet I: The War Begins (PC, not technically Trek, but had enough of the same flavor that I count it)
Star Trek: The Rebel Universe (PC, DOS)
Star Trek: The Promethean Prophecy (PC, DOS, got this after The Rebel Universe even though it came out before)
A homebrew multi-sci-fi franchise RPG that borrowed most heavily from Star Trek, Star Wars, and BSG (TOS) with rules based on half-remembered D&D rules. (Tabletop RPG)
Star Trek: 25th Anniversary (PC, DOS, one of the best PC games ever, much less Trek games)
Star Trek: Judgement Rites (PC, DOS, great game, but honestly, my memory kind of bleeds this and the 25th Anniversary game together)
Starfleet Academy: Starship Bridge Simulator (Super NES. Very enjoyable, and I actually beat it, too.

)
Star Trek: The Next Generation Interactive VCR Board Game - A Klingon Challenge (VHS. "Experience Bij!"

)
Star Trek Customizable Card Game (collected some cards, but never played)
Star Trek: The Next Generation – A Final Unity (PC, DOS, one of the best PC games ever, much less Trek games)
Star Trek: Klingon (Windows. I remember this being alright, and not much more about it.)
Star Trek: Borg (Windows. I remember this being buggy as heck, and not much more.)
Star Trek The Next Generation Roleplaying Game (Tabletop RPG, got the sourcebook and a few accessory books. Never played - the system *sucked*)
Star Fleet Battles (Tabletop Wargame. Played once with highly enthusiastic friends. I know this will be blasphemy to many here, but I hated it. Too much number crunching for not enough fun, and the feel of Starfleet was all wrong.)
Star Trek: Starship Creator (Windows. Too limited.)
Star Trek: Armada (Windows)
Star Trek: Starship Creator Warp II (Windows. Still too limited.)
Star Trek: Voyager Elite Force (Windows, another Doom clone. Bleh.)
Star Trek: Shattered Universe (Playstation 2. Mirror Universe stuff - a lot of fun.)
Star Trek: Armada II (Windows. A lot of people give the Armada games grief for being "bad Trek". Probably true, but my son and I had a lot of fun playing them multiplayer, so whatever.

)
Star Trek Online (Windows. This game is made by Cryptic Studios that also made City of Heroes, which I loved. And it is similar in a lot of ways, and I enjoy those. But the differences get annoying over time, the missions are too easy, and the overall story is on rails. I still log in now and then, play a little. And I'll give it this: it finally has a nice version of what I think they were going for with the earlier Starship Creator softwares.)
Star Trek Timelines (Android. I installed this just long enough to determine that it seemed very dumb and, like many "social games", like an attempt to separate me from money. Bleh.)