Batman has a rogue’s gallery heavy on the Dick Tracy style weirdoes, more of them to be confined to an asylum than a prison when he catches them. #1 is of course the Joker, Chaotic Evil to Batman’s Lawful Good. A great crook, a world-class murderer, and unfortunately a pretty bad comedian.
I’ve written bits here and there about building a recurring villain before, and noted that much of it is down to player reactions. Popularity will always be a factor. There’s character hate and then there’s player hate - if you get that, retire the character, at least for a while.
Like Batman himself, the Joker has risen and fallen in power, danger and Weird Level from a guy with a skin condition to a possibly-immortal avatar of chaos depending on the needs of the story. Apparently the Gotham TV series will have a different potential future Joker in every episode - which seems like a joke that will wear thin pretty quickly, but points to his mutability.
His motivation shifts around as much too, although flat-out killing Batman is rarely the issue. That’s a key part of his longevity - he plays by the same no-killing-the-enemy rule Batman sticks to, except in the most grimdark variations, despite racking up an impressive bodycount of anyone and everyone else.
And of course, he has a great shtick. Clowns Are Scary is one of the classics. (I just Googled Clowns Are and it suggested Scary first.) And as Tim Burton noted in 1989, ironic considering the hero dresses up as a bat to try and scare people.
So where does this leave us? A variety of stories the villain can be used on, playing by the same rules to prevent complaints about unkillability, and a shtick. Sounds easy... but there are plenty of unsuccessful villains that prove it takes luck too.