Two-Face. The two have actually had quite a bit of a rivalry.
You see, Joker beat up Harvey (before he became Two-Face) in front of his wife one time, and it's something that I feel Harvey has never forgotten, and he has referenced it several times. They actually did trade blows at one point in Dark Victory. Two-Face beat Joker up as revenge in front of the other baddies in an attempt to prove his worth to them, something that actually impressed Joker. However, Joker later got his own revenge when he shot Harvey.
In Death of the Family, Joker really messed with Harvey to the point where he almost convinced him how idiotic his dependency on his coin really is.
In Arkham City, there are several references to the fact that Joker's and Harvey's gangs are at war with each other. Face has been attempting to take over Joker's territory for a while.
Other than that, Riddler isn't too fond of him, simply because he feels that Joker is too chaotic and savage compared with his more intellectual approach to dealing with Batman. Riddler doesn't consider himself insane, but quite the contrary actually because insanity implies a form of mental illness, and Nygma considers himself to be an intellectual, and so, he doesn't respect the insane Joker.
We know Jason Todd aka the Red Hood (if you want to count him as a villain) hates him for obvious reasons.
I'm not sure about Penguin, but as businessman who likes to control things, he certainly isn't too fond of Joker's random and unpredictable killing sprees, as they are bad for business.
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