I've noticed that that I get more upset about some criticisms of characters than of others, but it isn't always based on which character I like. For example, in Torchwood fandom, I'm quite tolerant of hostility towards Owen (as long as fans don't get nasty about his physical appearance), but I have a very low tolerance for Gwen bashing. And this despite the fact that I like Owen quite a bit more than I like Gwen. In BtVS fandom, I've been quite disturbed by the comments I've seen people make about Riley (I once saw someone describe him as "the most evil character on the show", which struck me as a little twisted), despite that fact that I don't really like Riley. But while I have more positive feelings toward Willow than I do towards Riley, I don't get nearly as bothered by criticism of her.
And sometimes I have these kinds of inconsistencies with a single character: my favorite incarnation of Spike is ambiguous Spike in BtVS S5-S6, but I don't mind it when people say unfair things about him. But say a single unfair word about my LEAST-favorite (but still beloved) incarnation of Spike, newly souled S7 Spike, and I find myself getting very defensive.
Here's a list of my favorite and least-favorite characters and pairings in each fandom, and my perception of what fandom's favorites and least-favorites are. I'm not doing my RPF fandom because deciding who qualifies as a character in an RPF fandom makes my brain hurt, as does deciding who qualifies as a fan (If you like the music but aren't interested in the biography are you still a "fan" in that fandom?).
My favorites: Owen, Jack is a close second. I identify most with Tosh, but she’s not quite a favorite.
My least-favorites: I love everyone on the main team, but Gwen and Ianto are tied for last. Also, I never really attached to any of the Miracle Day newcomers (although I liked just about everyone in Children of Earth). My least-favorite recurring character is PC Andy.
Fandom’s favorite: Ianto, maybe Jack.
Fandom’s least-favorite: Gwen.
My favorites: Jack/Martha, Owen/Dianne.
My least-favorites: None.
Fandom’s favorite: Jack/Ianto.
Fandom’s least-favorite: Jack/Gwen.
My favorites: Buffy, Faith, Spike are my darling pets. Oz and Cordy, also make the list.
My least-favorites: I like everyone, dammit, but: Tara, Anya, Riley.
Fandom’s favorites: Spike. Probably Oz. Maybe Faith.
Fandom’s least-favorites: Buffy, Riley, and Dawn get the most hate. Buffy also gets a lot of love, which complicates things. Oh, and Kennedy isn’t exactly Miss Popularity.
My favorite: Buffy/Spike.
My least-favorite: Buffy/Angel. I warmed up to them after they broke up, though. I like most pairings.
Fandom’s favorite: Buffy/Spike.
Fandom’s least-favorite: Buffy/Riley. Maybe Willow/Kennedy?.
My favorites: No consistent favorite. At various times, depending on the season, Cordy, Faith, Lindsey, Darla, Angel, Wesley, Justine, Connor, and Spike have all made the list.
My least-favorites: Probably Lorne. Fred and Gunn are pretty low.
Fandom’s favorites: I’m not as familiar with AtS fandom as I am with some fandoms, but I get the impression that the popular characters are Lindsey, Lilah, Wes, and Spike.
Fandom’s least-favorites: Again, not as familiar as with some fandoms, but yeah. Fred. Women who have the affection of popular guys are the source of all evil in the universe, aren't they?
My favorite: Angel/Darla.
My least-favorites: Angel/Cordelia or Cordelia/Groo.
Fandom’s favorite: Wesley/Lilah, I think.
Fandom’s least-favorite: I think Wesley/Fred.