I've played almost every Trek game in existence. I think my first was Star Trek V on my Tandy 1000TX, and I loved the starship "sim" part. Funnily, apparently this part was a "simulation" because the Enterprise could not be blown up in a game.
Most memorable for me:
25th Anniversary (PC) - how can this not be a favorite? I remember anticipating this game's release. Then I was horrified when my Tandy 1000 didn't have enough RAM to run it so I had to wait until I got a 486 PC.
25th Anniversary (NES) - totally different, unique adventure game
A Final Unity - Same deal as 25th Anniversary. Amazing TNG experience.
Future's Past (SNES) - Has some similarities to AFU.
KHG - Klingon perspective, Unreal engine surreal. This was one bleeding edge Trek game at the time.
TNG Interactive Technical Manual - it's not a game but I can photo-realistically explore the E-D! It even has the right ambient sound effects.
Dominion Wars - sort of weak, but it has Jeffrey Combs and Marc Alaimo (!!), and decent combat. Can play as Feds or Dominion.
DS9 The Fallen - amazing atmosphere. Somewhat explorable DS9 and other cool locales.