I have narrated Star Trek games using everything from Over The Edge (I was in one of the original playtesting groups, and hence am quite fond of the game) to Time Lord to FATE (a terrific FUDGE variant) to Risus (S. John Ross of course wrote the Andorians book for ICON, a book as dear to my heart as John M. Ford's Klingons book for FASA) to a nearly freeform set of rules called Maximum Game Fun. These have proven great for convention games, since they do not require that the player be experienced or even a roleplayer at all. In fact, I once designed a MGF scenario called 'Crisis of Infinite Wesleys' for Penguicon, a local convention, specifically to coax Wil Wheaton himself into playing. Wil had to cancel his appearance, alas, so the game never ran.
“In our every deliberation, we must consider the impact of our decisions on the next seven generations.”
-- Great Law of the Iroquois Confederacy