Whether or not you count Captain America as a trilogy is up to the individual person. Don't think we're going to come to an agreement on that one so people can include it if they think it's a proper trilogy or not (if they think it's part of a larger whole.)
OK, so here are mine. I'm sure there are other trilogies I forgot but these are the ones I can think of.
1. Captain America: The only trilogy that actually delivered three quality films.
2. Blade: I might say that Spidey is "better" but I have to give the #2 spot to Blade because I own Blade 1 & 2 and I don't think I own a single movie from any other trilogy. Let's pretend #3 didn't happen.
3. Spider-Man: 3 absolutely sucks but I'd put the first two films up against any other first two films of a superhero trilogy.
4. The Dark Knight: I hate Rises and think Dark Knight kind of stumbles at the end but it's still gotta be up there.
5. Superman: I'm a big fan of #1 and #2 and while I don't remember much of three, the woman getting sucked into the machine and becoming a robot still haunts me. It's right up there with Dark Knight but I haven't seen them again in a while so I'll hold off of putting them up there.
6. X-Men: X2 carries it as the third film is ass and the first one doesn't really hold up as well as I thought it would.
7. Iron Man: I don't like the final act of 1, not a fan of 2 at all, and barely remember 3 but Robert Downey Jr. charms his way into the 7th spot.
8. OG Batman: I almost don't want to call this a trilogy because Burton only did two but I really like Batman and Batman Returns is OK. Forever is a huge misfire.
Honorable Mention: Hellboy, which would be up there if they delivered a good third movie.