The Animated series is by far the best adaptation in my opinion. It's Action-packed, suspenseful, dark, and even funny at times. It just does everything right.
I especially love how they handled Harvey Dent and his transformation into Two-Face.
And lest we forget, the animated series gave us the incomparable Harley Quinn. That would be a default win even without all the other awesomeness.
I liked it a little better before it made the switch to the New Batman Adventures. The writing was still exceptional, but they changed the animation to sync up with the rest of the DCAU. The original animation had this very dark, film noir style to it which I absolutely loved.
But one of the greatest contributions was Mark Hamill as the Joker. Heath Ledger was a good actor, and did well in the Dark Knight (even if I don't really care for the movie or how they portrayed the character), but he's not who you think of when you picture The Joker. When you read The Killing Joke, or A Serious House on Serious Earth. Ledger's isn't the voice you hear. It will Always be Mark Hamill. The Ledger Joker was an interesting interpretation, but The Animated Series Joker is an icon