When Batman came out in 1989, it was a reboot not just for Batman, but for superhero movies. Only Superman had been any good as a movie, and even that series was too campy for a lot of folks. the 1989 Batman hit the sweet spot of a darker mood, solid action sequences, but still plenty campy. Jack Nicholson was amazing in it, playing himself. It was a great movie for its time. Comic book films that followed immediately in Batman's footsteps: Dick Tracy, the Mask, The Rocketeer, Blade, the Crow, and others.
The movie hasn't held up super well for two reasons: (1) superhero movies got a lot better later, but I think you can credit this film with leading to that; and (2) the initial sex scene with Kim Bassinger is pretty creepy by modern standards. Maybe I'm too PC about it, but...ick.
Batman Returns (1992) was also pretty solid, and Michelle Pfeiffer as the Catwoman...yikes. If you're not into her, you're probably gay. Not that there's anything wrong with that. :-)
That movie, unfortunately, spawned one of the worst movies ever made on a big budget: Catwoman. The thinking, if there was any, was take a smoking hot Halle Barry, put her in a similarly hot outfit (though, frankly, not as good as the Michelle Pfeiffer version), and make another sex symbol, Sharon Stone, the villain. Put all your money and thinking into the casting, and forget about the rest of it. Oof. What a wreck. Unfortunately, I've seen it, but I wish I hadn't.