I enjoyed The Matrix and The Matrix: Reloaded, although I don't know if I'd go as far as to classify myself a fan.
The first one's guilty of a helluva lot of exposition, particularly when Laurence Fishburne is telling Keannu Reeves the background of the story.
As a writer I'm told to avoid exposition at all costs, that characters have to find out information, as opposed to being told. And yet here, for 15 minutes, Laurence Fishburne lays down the story so the rest of the movie can proceed.
Thought the second one was also a backward set in the character development of Keannu Reeves. In no fight sequence should he have been troubled after what was established toward the end of the original Matrix. In fact, he could've just stood there and absorbed all the punishment dealt.
That's essentially what I don't like about the second one - there's action not for the sake of the story, but for the sake of these guys proving they're nifty.