Arkham Asylum is my favourite, it had the best story and having everything in a tight and neat location really did help. Batman is stuck on Arkham Island with most of his villains, and it's a great game. The feeling of first playing it was exceptional, I really had never played a superhero game that good before.
Thing is, it's hard to go back to Asylum because the gameplay has progressed. I do love City and Knight, but they're a bit broader and I think the game loses something. Then again, it was necessary to move away from the asylum and into Gotham city. I consider Arkham City to be a bit like the Aliens/Terminator 2 to Alien/Terminator. I like it only a minuscule amount less than Asylum, but because it moved the gameplay along I can't go back to Asylum without it feeling a bit outdated.
I didn't play Origins. Maybe I'll work my way back to it.
I liked Knight, but it had too much in it and the Batmobile stuff didn't quite work. I did like roaming around the larger city, but there was so much going on that I felt it had too many things trying to take focus.