Man, there seems to be no end to the free Star Trek RPGs that exist on the net. Finding them and giving them a quick look was a good way to distract myself this morning. Here are the two that stood out to me...
Far Trek
Looks fast paced and quick to get into. Seems to have a decent amount of support.
Where No Man Has Gone Before
Uses the Micro20 system which looks pretty slick. I like how it handles ship combat, at least as the brief glance I gave it.
Obviously I haven't played either of these but I think I'm gonna give one or both of them a shot with some friends. They both look fairly dynamic and interesting.