Crippling Barbara Gordon was certainly a hoot, but the greatest Joker moment was when he beat Robin (Jason Todd) with a crowbar and blew him up.
Two events have shaped Batman. The first, of course, is when Joe Chill murdered Bruce Wayne's parents. The second was the death of Jason Todd, an event that, until recently, seemed could never be undone. The death of Robin forever altered the Dark Knight and signaled a change in comics as a whole. Could anyone else have perpetrated such a horrible crime? No, it wouldn't have felt right to have any other villain whack the Boy Wonder. And that's why Joker is the greatest Batman villain of all time.
The Clown Prince of Crime is the mirror opposite of Batman. As much as Batman fights for order, Joker battles for chaos. He's irrational, unpredictable and -- as his creation -- ultimately the responsibility of Batman. If every villain in Batman's Rogues Gallery were to be wiped out and only one could be saved, the Joker would be that one. Any other villain can be replaced, but the Joker is timeless. Without Batman there is no Joker and without the Joker, there's just no humor in Gotham City.