Batman: The Animated Series, FOX/WB (reruns on Disney XD)
Absolute Anime; Disney XD; IMDb; official website; Retro Junk; TV.com; TV Tropes; Warner Bros.; Wikipedia
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Bruce Wayne: orphan, billionaire, businessman, playboy, philanthropist, superhero. He is the Batman. He is the coolest superhero ever. Period. He has no super-powers. He is not a metahuman, he is just a man. He is exceptionally clever, a brilliant detective, he has trained for many years to hone his fighting skills (both Eastern and Western) to near-perfection. He has tons of extremely cool gadgets, from batarangs to the Batmobile, Batwing, of course the indispensible utility belt, and countless other things. He has a few friends, of course. Dick Grayson, the first Robin, eventually became Nightwing. Tim Drake, the second Robin (in this series). Alfred Pennyworth, Batgirl (Barbara Gordon, who we like), Commissioner James Gordon. He also has some of the coolest enemies, including the Joker, Harley Quinn (who we like), Catwoman (who we like), the Riddler, the Penguin, Poison Ivy (who we like), the Scarecrow, the Clock King, Two-Face, Ra's al Ghul, and the list goes on and on. Oh, it's all very dark and stylized and clever and dramatic and often funny. Always cool.

What else can I say? I thought the characters looked better before the show got ultra-stylized or whatever. Or was it less stylied, or just a different kind of stylized? Whatever. Still very cool. ...Actually, though I wasn't aware of this at the time, apparently that change in the animation style reflected a new spin-off series, albeit in the same continuity, called The New Batman Adventures (IMDb; official website; TV.com; Wikipedia), aka Batman: Gotham Knights. It was also run as part of The New Batman/Superman Adventures. Whatever, I think of it all as pretty much the same thing. Anyway, I'd like to say a great deal more about The Animated Series, I just don't know what. Except that it's probably my favorite incarnation of Batman (and related characters) ever, in comics, TV, film, or any media. Oh, and of course the theme song, based on the one Danny Elfman composed for the 1989 live-action Batman movie, was very cool.

Some direct-to-video movies include: Batman: Mask of the Phantasm (IMDb; Wikipedia), Batman & Mr. Freeze: SubZero (IMDb; Wikipedia), and Batman: Mystery of the Batwoman.

DCAU
It's also important to note that this series was the start of an ongoing group of animated series collectively known as the DC Animated Universe (Wikipedia), which share a continuity. The others include Superman, Batman Beyond, Justice League, Static Shock, and The Zeta Project. There are also a number of comic book series based directly on these properties, with similar art styles, though I wouldn't consider the stories in these comics to be canonical within the DCAU....