I know this came out in the 90s, and it is referenced constantly, and everyone and their grandmother already knows how great it is, but The Long Halloween is really, really good.
This events of this novel take place relatively early in Batman’s career, having worked with Lt. Gordon for some time but with a seemingly new relationship with DA Harvey Dent. There is a turf war between two rival crime organizations, and Gordon and Dent are struggling with how to best deal with these threats. Dent and Batman try to take matters into their own hands, but the gangs find out that Dent is involved and blow up his house, injuring himself and his wife. Afterwards, a mysterious vigilante kills one the villains on major holidays, carefully leaving themed tchotchkes at the scene, and thereby earning the nickname the Holiday Killer. Throughout the ensuing years, the reader sees many of the regulars from the Batman universe including the Joker, Catwoman, and a host of other at Arkham Asylum and out in the wider world. The killer(s) are eventually revealed, but the book builds the tension towards the ending, where Two-Face is introduced.
The story itself is set up cleverly, with each individual episode built around the given holiday and associated murder, making the passage of time easier to follow than it is in some novels. This book is great not only because it is a well written Batman story, but also because it is a pretty good murder mystery as well. It has a lot of atmosphere, and gives some great backstory for both Dent and Batman, particularly with the relationships he develops with others. I am going to seek out the sequels written by Loeb and Sale, as this might be one of my favourite superhero graphic novels ever.