The trouble with Trek
Watching the movie, there is a great deal of potential in the "new" Trek continuity. The kind that makes me consider the possibilities, especially since one of my long-term campaigns is on yellow alert.
The problem is two-fold. First of all, Star Fleet is a military organization. Anyone that has had to ride herd on a bunch of PCs knows how good they are about following orders. When my group discussed a campaign set in the Battlestar Galactica universe, the first thing I brought up was that Adama wouldn't put up with their usual crap.
Plus there's the whole command structure itself. Some characters will outrank others, even in the most mature of groups this could cause problems. While my group has worked well in Firefly with one character being the "captain" it was a lot more lax than an actual military.
Finally, it's a lot harder to run my typical "sandbox" game, where I try to give my players a fair amount of freedom and throw in some plot hooks. A Trek style game is a lot more narrative, which means more prep.
Of course, it may all be moot. I'm hoping things don't head south in my current game, and even if they did Trek might be pretty far down the list of campaigns my players would be interested in.