[Eliza Shipwrecker]

James Bond is a series of movies featuring the same character(s), but each one capable of stadning alone. A trilogy is a sequence of three movies that advance a storyline from one movies to the next.

It's hard to pick a "best" trilogy, because it's difficult to compare different genres against each other. I think the trilogies listed are among the best (and I agree that Star Wars doesn't qualify - though I love the movies), for different reasons, but I would also add:

The Matrix
Indiana Jones (at least until another one comes out)
Ocean's Eleven, Twelve and Thirteen