Batman: The Animated Series, on FOX
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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 indispensable 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), Commissioner James Gordon. He also has some of the coolest enemies, including the Joker, Harley Quinn, Catwoman, the Riddler, the Penguin, Poison Ivy, 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. Oh, and of course the theme song, based on the one Danny Elfman composed for the 1989 live-action Batman movie, was very cool.
The New Batman Adventures, on The WB
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This is alternately considered either a spinoff of "Batman: The Animated Series" or the fourth season of that show. It was also run as part of The New Batman/Superman Adventures. Whatever, I think of it all as pretty much the same thing. I'd like to say a great deal more about both The Animated Series, and TNBA, I just don't know what. (But there was a somewhat different look to the animation in the latter show.)