"Spirit of the 24th Century"
As I mentioned elsewhere, I have toyed with the idea of building a Star Trek campaign around Evil Hat Productions' FATE 3.0 game engine, the same rules which power Spirit of the Century and are slated to bring Jim Butcher's The Dresden Files to life. Character creation in SotC is especially interesting: everyone has three phases in which they briefly outline their origins, what they did in the Great War, and their first grand adventure (their first 'novel'). The last two phases are their 'guest appearances' in the novels of two of the other characters.
Adapting this for Star Trek, the first phase remains tied to the characters' origins and the second could be what they did in Starfleet Academy. The third would be a notable tour of duty or mission, with the fourth and fifth phases being tours/missions in which they served alongside another character. Definitely room for some interesting character development, and the characters needn't be limited to five phases with two Aspects per phase as in SotC. A ten-phase character with one Aspect per phase would work as well, and give characters a little more breadth of detail.
Part of the utility of the FATE 3.0 rules is that they can easily take a page from the Serenity roleplaying game and stat out starships much like a character. The ship's Aspects could be tagged or compelled just like a character's, and its Skills could serve to modify those of the characters' during missions. Material from the assorted Trek rules sets could be mined for inspiration, providing plenty of Aspects, Skills and Stunts with a suitably Trek-ish flair.