What TV Tropes labels as "Unintentionally Sympathetic" characters, is rather self explanatory. It refers to any characters that audience are is supposed to oppose (and more often then not, declared to be in the wrong by the narrative), but their actions and behaviors within the work often paint a different picture. In other words, what are some particular characters that are meant to be rooted for, but you can't help but sympathize with them? What has led to you to root for those characters?
I'm not sure I'd say 'rooted for', because by the opening of the book he's already a mass murderer, but I always felt really sorry for Kevin in We Need To Talk About Kevin. I think it's possible just clumsy writing, but his mother seems to label him 'wrong' pretty much from conception based on hardly anything. There's one point in particular which stuck with me, when he's very small and she's upset because he won't roll a ball back to her. She uses it as evidence of his general brokenness, but all I could think when I read it was 'maybe the kid just doesn't like balls, did ya ever think of that?'. In general I think that book is a great example of how narrative voice can really influence reader perception of the same set of facts. Edit: I should say I feel sorry for Kevin as a young child. Once he reaches the age of animal and sibling torture, all bets are off.
I'd have to go with Morgana from the TV show Merlin (spoilers). In later seasons, she's supposed to be irredeemably evil, an unhinged mass-murderer without a conscience. However, it's such a jarring contrast with the early seasons, where she's straight-up heroic and kind, and her very sympathetic initial transition to the dark side (that the protagonist is largely responsible for), that it never feels genuine. Thus, even when the show writers were desperately trying to show how much of a card-carrying villain she had become, she stayed sympathetic. I'm pretty sure this was just clumsy writing, they gave us too many reasons to root for the final villain, to the point where early into her villainy you're tempted to root for her over the protagonist, then had to back peddle hard and overcompensate by trying to make her as unsympathetic as possible, and it didn't work.
I like all the creeps from Breaking Bad. Even Gus (because he was so dapper) and Todd (because he was so polite).
I gotta admit I kinda liked Tucco (if that's how you spell it?) just because he was so elemental and such an unremitting badass. As they say, to have a great story you gotta have a great antagonist.