This question originally appeared on Quora.
By Laura Michet, computer game writer
There are currently fourteen comic books about Batman, Gotham, and Batman's subordinates/family members in print today. If you want to read good Batman stories that don't require "catching up" with a year or more of comics, I'd suggest staying away from the comic issues that are currently in print and reading some of the older classics of the Batman corner of the DC universe.
Begin by reading Batman: Year One, written by Frank Miller. It's an influential "reboot" of the story that took us back to Batman's roots and the story of the first year he spent under the cowl. It influenced the movie Batman Begins. It was recently published in some kind of "super edition" or collector's edition or something-- so you can probably find it at your local comic book shop on the rack of recent hardcover releases.
Next, read The Long Halloween, by Jeph Loeb and Tim Sale. It is my favorite Batman story, and it has earned classic status. It is a superb mystery, has fantastic art, and takes us back to Gotham "before it got crazy"-- most of the enemies are gangsters, not supervillains. It also influenced Batman Begins. Follow it up with its sequel, Dark Victory, which is also pretty good.
Once you've read these, it's time to read a crazier take on the Batman universe -- Gotham by Gaslight, which asks the question, "what if Bruce Wayne lived during the Victorian era, and Batman had to solve the Jack the Ripper mystery?" It is illustrated by Mike Mignola, the artist behind Hellboy, who is my favorite living comics creator. It's wonderfully atmospheric and is a good (very quick) read.
Next, get a little more bizarre and read The Dark Knight Returns, Frank Miller's incredibly famous take on Batman-as-old-man. It is, rightly so, considered one of Frank Miller's best works, and one of the best superhero graphic novels ever, period.
Finally, finish up with The Killing Joke, Alan Moore's famous Batman story, which pits Batman against the Joker and his extreme sadism. It's also short. It's not one of my favorite stories, but many people adore it, and it's certainly a classic. It features Commissioner Gordon and his family. It's one of the best depictions of Batman's bizarre relationship with the Joker.
Edit: I can't believe no one called me out about including Morrison's Arkham Asylum! (And I can't believe I forgot about it last night!)
This is Grant Morrison and Dave McKean's Batman magnum opus -- a baffling, terrifying, thematically-dense exploration of madness. Depending on your temperament, this may or may not be a good book to read in your first pass on Batman books. I read it very early in my exploration of comic books, and I LOVED it because it was so goddamn wild, but if this isn't your thing:
... then you should probably save this book for later on in your Batman-reading career. Be advised, though: it's very very very very very good. So you should definitely give it a shot.