Tim killed Poison Ivy when he was under the identity of Red Hood, back in Season 2 or 3. Ivy eventually came back through her powers, but hasn't done much since.
The Joker's history is pretty thorough. He found out where Oracle's Clocktower was and attacked her when she was trying to get her ability to walk back, which led to his discovery of Batman's true identity. Ever since, it's been about personal jabs at Bruce, for the most part... even going as far to bury Bats alive with his parents' corpses.
Two-Face was controlling the mob for awhile, before he was cured and became Harvey Dent again. Now he's scarred once more, and hunting the 'new' Batmen as a vigilante working with Gordon.
The Riddler threatened to bomb Bludhaven in one season, and was running from the mob in another, but that's the extent of what I remember about him. I put him into the detective phase he currently has in the comics.
The Scarecrow's role never got larger than what he did last season with Jason Todd, though he was The Scarebeast in Season 2 for a brief time.
Harley Quinn was pregnant in Season 2, but Joker killed the baby. Eventually she went back to him, which led to her being viciously beaten by Black Canary. After Joker's apparent demise last season, she renounced her ways as a criminal and helped Batman as a vigilante, simultaneously having a weird crush on him. Whatever happened to her following his death is unknown.
Killer Croc and Nightwing were enemies for awhile, during my run. He and The Joker teamed up a couple of seasons ago, when Croc was being held captive, but I think that's the extent of his deeds.
Mad Hatter has... superpowers now, I think. I'm not totally sure, to be quite honest with you.
That's what I know of the major ones.