Batman had always been my favorite costumed superhero for a lot of reasons. For one thing — Bruce is just “this guy” – he’s not an alien from another planet, he wasn’t bitten by a radioactive spider or exposed to Gamma radiation. He’s just a guy turning his own personal tragedy into an attempt to do something good for his city. Which makes it a bit more realistic than other superhero books. Now you still have the over-the-top villains, and futuristic tech, but Batman is much more down-to-Earth than the majority of comic book heroes.
Second, I’ve always been a fan of mysteries, including film noir/hard-boiled detective fiction. And Batman, in concept, is closer to Dashiell Hammett than Superman or most other super-heroes. True, most traditional detectives don’t run around in capes, masks, and tights catching bad-guys. But you could easily take Bruce’s backstory (the death of his parents) and make him a private detective or cop and it wouldn’t really change the story or Bruce’s personality. After all, one of Batman’s titles is “The World’s Greatest Detective” and DC did, originally, and still does, stand for “Detective Comics”.
The other thing is that Bruce’s entire motivation is that he wants to see that what happened to him, never happens to another child. He’s not motivated by vengeance. If Bruce was motivated by vengeance he would have found the guy who killed Martha and Thomas Wayne and killed him, then a few years later found the guy who hired the guy to kill Thomas Wayne and killed him too. But, never in canon, or in any of the “slightly non-canonical” graphic novels does Bruce ever seek out strict vengeance. He’s out there protecting Gotham and it’s citizens. He gets angry with the various Robins when/if they go over the line (esp. Jason Todd). Bruce also doesn’t use guns and turns over the bad guys he catches to the police. Not exactly the vigilante he’s sometimes portrayed as.
So, you have an angst-ridden, hero – often suffering from horrible Survivor’s Guilt and PTSD, but who still attempts to turn that into something positive. I find that inspiring in a superhero. Bruce has his faults, which make him more human too. (Superman, for example, always seemed “too perfect”. Not only completely invulnerable to everything bar Kryptonite, but as a person/character Clark always seemed to perfect. Please don’t flame me.) But Batman rocks in whatever specific universe you find him. I love the Nolan films (Batman Begins, The Dark Knight, The Dark Knight Rises). I quite enjoy the DCAU (Batman: The Animated Series, Justice League, Justice League Unlimited, Batman Beyond, various films). And I’ve enjoyed many of the Batman graphic novels (too many to list) and soft-bound books.