As the cliche (doesn't) go: Where there's the box office smoke, there's going to be sequel fire, and Batman's box office breaking lead to three follow-ups that pretty much define that whole The Good, The Bad and The Ugly idea.
There are many who think that Burton's second Batman is his best, and I have to admit that I'm one of them. For one thing, it's just weirder, dropping a lot of the compromise from the first to form a messier, funnier movie where Keaton doesn't have to fight for attention next to a scenery-chewing Nicholson (Not that Danny DeVito's Penguin isn't almost as bad). Yes, it doesn't have the clearest narrative in the world, but I fully and only slightly shamefully admit that the 17-year-old me didn't care about that as long as Michelle Pfeiffer's Catwoman was onscreen.
Burton vacated the director's chair for the third movie (He stuck around as producer, however), leading to Keaton also leaving the series to pursue "more interesting" roles. Enter Joel Schumacher and Val Kilmer, and the beginning of the end. You can see the potential in all of their choices, even as the execution didn't live up to it: Trying to go for a new visual aesthetic instead of aping Burton was a good idea, but the neon dayglo look they came up with definitely wasn't. Similarly, the media-mocking of the plot (The Riddler's television-replacement device literally being an idiot box and sapping the intelligence of its audience) had potential, but the overly broad acting of Jim Carrey as the Riddler and Tommy Lee Jones as Two-Face brought everything down to a farce-like level that reminded people a little too much of the Adam West days.
Batman and Robin
...And this was where the franchise ended, thanks to Schumacher's attempts to "homage" Adam West and Dick Sprang going horribly awry. To his credit, the director apparently wanted the movie to be much more like a cartoon than the earlier installments, but with toy companies having input into the design of the movie's costumes and characters this time around, maybe things got a little out of hand from his original intentions (Whether the toy companies were in favor of the much-ridiculed nipple additions to the Batsuits is unknown, if unlikely). Not helping things was the arrival of Batgirl, bringing the lead cast to a cramped five characters (Batman, Robin, Batgirl and two villains Mr. Freeze and Poison Ivy, the last two masterclasses in overacting from Arnold Schwarzenegger and Uma Thurman). And yet, despite Schumacher himself apologizing for the movie on an extra from the recent DVD reissue, there's something weirdly compelling about it. I demand a critical re-appraisal!