First and foremost, Kaliyo. Even when I first meet her she already annoyed me like hell. I said to myself "I will so enjoy eliminating you at the end of Hutta" but then to my terror I got her as a first companion. Not only that, I had to put up with her UNTIL Alderaan when I got the bug (which I was reluctant too take too but was happy to replace Kaliyo). In the end I decided to give her another chance and completed her storyline but my opinion of her only worsen exponentially. After completing all 8 storylines and seeing all companions, Kaliyo is by far the most annoying and disgusting companion in the game.
Then it is the Bone face with the head wrapped in the bandages (kinda stupid even from appearance point of view since he can't wear any of the cool hoods). I didn't want to take him as an apprentice and I agreed with Harkin completely. Yet the game did not give me an option at least agree with him on the matter. All the conversation options were either in support of the Xalek or just purely against Harkin. That really annoyed me.
Then there is Quinn. I know many ladies liked him but I was just reluctant to take him. Now I actually like imperial officer characters but he was just the annoying type. A complete opposite of Grand Moff Kilran, for example.
Oh and I didn't want Bowdaar simply because I hate wookiees.