So I'm starting off with a right royal one that seems almost universal. I'm the outlier here but I didn't mind Tegan and Adric as companions. I know that fans hated him for whatever reason but watching all his episodes I didn't mind the kid. Tegan also seems to rub a few fans up the wrong way too and I'm not sure why they don't like her.
The reason I didn't like Adric was just down to a couple of episodes that made him betray/turn against the Doctor, and I blame the writer for that more than the character. I also liked Tegan as well, she and Nyssa made a good team.
My own controv opinion; The Master is overrated and overused, and I really don't like how the Doctor is so friendly towards him, handles him with kid-gloves, spares him etc. He (they?) is a mass murdering evil a-hole, and the fact the Doctor doesn't act accordingly to him simply because he is a Time Lord just bugs the crap outta me. Apparently the Family of Blood warranted eternal damnation for the small-scale murders they caused, but the guy (gal) who does multiple genocides gets a pass because they're the same species? Yeah, I hate it. The Master is no better than a Dalek.