Well, there are obviously a stupidly large amount, concidering that Batman has been out and about since the late 30's. But I'm really big on Batman myself, and have read quite a lot, although I admittedly only picked up the hobby like a year ago (in a dedicated fashion, that is.)
The Killing Joke was a good place to start - I personally find it the best Batman book I've read, and there's a pretty general concensus it's at the very least in a top three of best Batman books. Other ones typically mentioned there are:
Batman: Year One by Frank Miller - I personally did not care much for the visual style of this one, but the story is without a doubt absolutely brilliant. It explains the origins of Batman (and is, at least along the big lines, considered canon)
Batman: The Dark Knight Returns and Batman: The Dark Knight Strikes Back by Frank Miller - Both are also worth checking out. They tell the story of how Batman might be when he's old. Pretty fascinating, although again, I'm not a big fan of the drawings.
Batman: Hush by Jeph Loeb - Introduced a new, major villain in the batverse. Loeb does some epic writing, and Lee is, in my personal opinion, the most bad-ass artist currently around. his visuals are absolutely stunning with fantastic attention to detail.
Batman: The Long Halloween, Batman: Dark Victory by Jeph Loeb and drawn by Tim Sale - two books set in the early Bat-verse (Year Two). They have much of the same feel as Miller's stuff (and build directly on it). Real dark, murder mystery-like. Some of my absolute favorites, as well.
Batman: No Man's Land - After Gotham has been decimated by an Earthquake and practically been left to its own, Batman returns to the broken-down society that is his home to set it right. It's in like 5 books and crawling on 1000 pages total, but it's pretty epic.
Batman: The Man Who Laughs - Like The Killing Joke, deals with the early days of the Joker. Good read.
Batman: KnightFall Trilogy (Broken Bat,Who Rules The Night, and Knightsend)- Introduced the supervillain Bane to the Batverse, and deals with the very central question: What happens if Bruce Wayne can no longer be Batman?
All the stuff Grant Morrison has written the last few years, starting at Batman R.I.P., for example (there's also stuff before that (The Black Glove, and Batman and Son - but I've not read that yet, myself), and especially his run on Batman & Robin - I personally think Morrison is one of the best writers I've read. His plots are crazy tight, and he's an uncanny ability to tie up so many loose ends in the most epic moments and reveals. The books deal with Bruce Wayne's struggle against himself, and the passing-on of the Mantle of the Bat (BTW; you might also want to look at "Battle for the Cowl" by Tony S. Daniel if you look at the newer stuff).
Those are my recommendations. Last bit of advice: if (read: when!) you encounter some minor character/villain/hero you don't know who is, just google the person. You will probably need some help keeping track of everyone. It's not that easy.
And enjoy a lovely hobby!