Enterprise: Asteroids is pretty much the first game based on Enterprise and is an adaptation of the classic Asteroids arcade game. You control the NX-01 and have to fight off Suliban pod ships, Klingon warships, and Romulan warbirds in addition to asteroids, of course. I love the little touches like impulse engine exhaust, different phaser/disruptor effects, and well designed ship images.
Star Trek: Tour of Duty puts you in charge of the Enterprise-D in a vertical (later horizontal) scrolling space shooter (like Galaxian and its many sequels/adaptations). You face a minefield, Jem'Hadar attack ships, and a final confrontation with a prototype Borg cube. Destroyed craft leave Starfleet symbols you can collect to spend on one of several upgrades, giving the game extra replay value. I blew a couple hours on this one the first day!