There are almost too many great Batman comics out there to list. I would recommend you start with Batman: Year One by Frank Miller & David Mazzuchelli. Follow that up with Batman: The Dark Knight Returns also by Frank Miller. Then there's Alan Moore & Brian Bolland's The Killing Joke, Jeph Loeb & Tim Sale's Batman: The Long Halloween and storylines like Knightfall and No Man's Land which are by various writers and artists and are available in trade paperback collected editions.

I agree with AgentC.
New stuff Paul Dini's Detective Comics, he wrote like 20 issues. All good, and most of them one shots. You can buy the trades.

Old stuff: Batman Chronicles, Vol. 1: Bill Finger, Bob Kane.