I didn't really have a big problem with Alistair. Granted his jokes were bad and he whining could be pretty irritating, but that never really made me hate him. It just made him feel more human actually. He wasn't perfect, but his faults didn't make me dislike him. I suppose that's because his faults didn't totally overpower the rest of his character. To be honest, Morrigan annoyed me far more with her constant disapproval. Though I didn't really hate her either.
Anyways, an example of a character I really hate is Reaver from Fable 2. He is a perfect example of how not to make a character. He is a pompous asshole that holds himself above you in every single conversation. He clearly acts like he is superior, and even when he tricks you and almost kills you he acts like it was just a harmless joke. These are the characters you usually end up killing or punching in the face. But no, not only does the game deny you any opportunity to get back at Reaver, but it actively promotes the idea that he is better than you. Normally you'll get the hint that the writers want you to think that characters like him are jerks. But no such indication is present in this game. Also I don't care if he is voiced by Stephen Fry. It doesn't change what Reaver is.
I'm also not particularly fond of Tali from Mass Effect. I don't actually think she is a poorly designed character like Reaver though. She's just a character I don't like due to various events in both games, mostly Mass Effect 2. I'll also admit that the amount of praise she gets also causes me to dislike her, but that's not the only reason. That just enforces my hate for her. I honestly don't get why so many people praise this selfish ***** to no end.