Villains almost always intrigue me in some way, even if I personally dislike and regularly ridicule them. That's probably what makes the characters fun. Or really pretty much any character you can poke fun at.
I like cynical assholes regardless of whether or not they turn out to have a heart of gold or are actually sensitive underneath it all. Or any portrayal of a flawed character that doesn't take itself too seriously. Odd or eccentric characters, too and I like to play those types as well.
I've also been interested in what I'd call 'Arnold Friend' type characters. Though the character from that story doesn't have a mentioned accent from what I remember, the characters I feel fit this "trope" always have some sort of Southern accent. Eddie Kreezer from Hick is a huge example. The "Southern gentleman" who turns out to be unhinged and was honestly creepy from the beginning but so persuasive that better judgment is ignored.