There was Vislor Turlough who was brought in by the Black Guardian. After three stories, he turned 'good' though, when he realised that the Doctor wasn't the villain that the Black Guardian had made him out to be.
Ace betrayed the Doctor in "The Curse of Fenric", but it turned out that the Doctor had manipulated her into doing so as part of his plot against Fenric. In the later novels, she became at least super-bitchy, if not evil, and ultimately ruined the Doctor's plans to groom her as his replacement, running off with a super-motorcycle to become Time's Vigilante.
Adam Mitchell turned greedy, if not evil, in "The Long Game". He's the only TV companion to be thrown out of the TARDIS for bad behavior.
Novel and audio companion Fitz was on opposite sides against the Doctor multiple times, although it's at least arguable that the Doctor was on the more evil side in each case. There were also three versions of Fitz, some of whom were evil.
Audio companion Elizabeth Klein was an unrepentant Nazi in some timelines.
There have also been lots of more minor betrayals. Rose saving her father in "Father's Day", or even Amy saving the star whale in "The Beast Below", could be considered betrayals, and the first one might even be considered evil, but that's a bit of a stretch. For a better example, in the novel Genocide, Sam deliberately helps an alien who's trying to stop the Doctor, even though she knows it will likely end in the destruction of humanity, or even of the entire universe--but the three all end up on the same side, and understanding and respecting each other, by the end of the novel.
In "The Curse of Fenric", Ace did not intentionally betray the Doctor. At one point she did act against his interests but that was because (a) she let her enthusiasm run away with her and (b) the Doctor had failed to tell her enough about the situation for her to know that what he did was against his interests. The moment she found out that he had not wanted Judson to know what she'd told him, Ace warned the Doctor about what had happened. Later on, she gave him a vigorous telling off for having kept her in the dark, something she never liked and often complained about. On this occasion, though, she wasn't just annoyed, she was enraged. The reason she was so angry was because she had unknowingly done exactly what she least wanted to do and it was the Doctor's fault. However, he had not "manipulated" her into doing it; he'd just made a mistake.