I guess River Song would have to come into that category. I think now her story is known she's better understood, but even when we didn't know who she was, I liked her. Yes, she was a bit full of herself, and it was annoying that she knew more about the Doctor than we did and wasn't backward about telling us so, but she was clearly clever, brave and loyal. That repeating, haunting "I'm sorry, my love" in the Big Bang shows us that her feelings for the Doctor are 100% genuine.And of course she had already sacrificed herself in the Library.
Ace irritates some - and, certainly, there are moments during Dragonfire when you just want to shake her. However, she too, is a feisty and brave girl, clearly deeply affected by a crap childhood.
The Sixth Doctor also gets a rough ride from many people. Yes, the outfit was god awful, he was loud, egotistical, volatile, but Colin Baker portrayed that character extremely well. He was still, despite all the bluster, at essence our Doctor. I really must get round to listening to some of his Big Finish stuff as apparently the influence of a good companion, Evelyn Smythe, makes him a bit less highly strung.