I credit the original Blade with kicking off this generation of superhero movies. You can make your case for Batman '89, but I think it was Snipes' and Norrington's serious take on the hero, present in a modern day where people didn't know about the supernatural element, that set up the "superhero in the real-world" story.
Blastr cooked up a great article about this. Enjoy!
Edit: Here's an article about Patton Oswalt detailing some of the problems surrounding Blade: Trinity. Apparently most of the wide shots of Blade were done by a stand-in, and the lack of Snipes' presence made Ryan Reynolds have to carry the bulk of the film. A lot of his snark was ad-libbed, which, incidentally, is why I actually liked the film.