Our criteria here involved people with superpowers, so technically, a perfectly normal human such as Batman wouldn't qualify for this list.
Let me preempt any objections, however, by claiming that being a billionaire is a superpower at least on par with the ability to turn small fires into big fires or having equivalent spider-strength. With that out of the way:
5) The Crow: By rights, Spider-Man 2 should go here, but I'm going to throw a bone to the melodramatic, cheesy, and undeniably fun brand of superherodom that existed before we were rescued by the '00s. And The Crow is nothing if not perversely funny and cartoonishly gothic. It's also pretty good. Try to resist its gloomy-gloom cityscape and portentous dialogue all you like, your efforts will be as powerless as a common street thug against the invincible resurrected corpse of the wrongly murdered.
4) X2: I'm going to go ahead and say this is the father of the modern superhero movie, the first to effectively combine emotion and realism with beatings and eye lasers. A 5-year-old father might strike you as unnatural, but just pretend the genre got bit by a mutagenic retiree which accelerated the aging process several-fold. Anyway, juggling all these X-Men and X-Women within a coherent story is a feat in itself. Shifting alliances among the mutants ups the intrigue. Showing what you can do with a superhero once that creation story stuff is out of the way, X2 set the stage for a troupe of awesome sequels (and decidedly less awesome three-quels).
3) The Incredibles: Rollicking animation and a clever but heartfelt take on the family dynamics of the superhero team vaults this up with the best. Some argue its "We're special and you normals can't join us" undertones are fascist, but that just makes me like writer/director Brad Bird all the more for running against the grain. Even when you disagree with its conclusions, good art earns what it wants to say.
2) Iron Man: Other than repeating my full name twice, "Robert Downey Jr. as Tony Stark" might be the six most beautiful words in the English language. Director John Favreau complements Downey's unstoppable comedy machine with some hilarious physical jokes of his own. The look on Downey's face when he's finally blasting into the sky captures the glee of being more than human in a way few hero movies do. It's good to see a hero enjoying himself for once.
1) The Dark Knight: Say what you will about canonizing a movie less than a week old, but you will be totally, totally wrong. This is like the Raymond Chandler of superhero movies: nailing the best of what the genre has to offer while matching strides with the great dramas. Christopher Nolan's plotting is urgent and dense, there isn't a weak link in the cast, and the sense of menace is so cloying you can't scrub it off your hands even with that gritty industrial soap that could clean the dirt off a pile of dirt.
Movies such as The Dark Knight are why I go to the theater every week.