First, there’s The Dronelands War, mentioned in the comments, a spectacularly well-done propaganda film about the conflict between Red Alliance and Ethereal Dawn. It’ll make you want to run out and enlist with ED.
CrazyKinux includes a couple of official EVE trailers in his list, but he left off my personal favorite, the very early Eve Never Fades, which lacks the crisp high-res graphics of the newer productions, but makes up for it in ambiance and a great musical track.
Lastly, and most importantly, we have the most important EVE films ever made, Clear Skies 1 and 2. CrazyKinux may have considered them out-of-category, since they’re full-fledged machinima in their own right, and they use footage from the Half Life 2 engine for internal scenes.
Watch these in their entirety, if by some mischance you haven’t already. Either one is about as good as any episode of Firefly; highly entertaining with great dialogue, and while the productions are a bit rough, everybody involved is an amateur, and the voice acting is terrific with that in mind.