While it's dated I'll probably say "Elric", he's one of those popular but hated characters that got a ton of scorn when I first started playing D&D. Mainly because he's pretty much your typical Warrior-Mage (who uses very high powered ritual-pact based magic but is otherwise separated from his grimoires) with a really powerful magical sword who at the end of the day usually winds up killing everyone either unintentionally or stabbing them in the back. That said I always felt he was a great character with the way he's set up, grappling with having the conscience of his human soul (but not it's memories) while part of a race that is supposed to have a fundamentally different emotional structure, and pretty much battling against a destiny he doesn't want to fulfill and being punished for it every step of the way. He was pretty much the "Dark Angst Ridden Hero" before it became a stereotype, and while not the first, he pretty much inspired most of them that came later. Most importantly though I believe "Elric" has to be judged in the context of the entire "Champion Eternal" cycle starting with "Champion Eternal" that explains why John Daker (the reincarnating hero) was in that position and comparing it and what happens to what transpires in the stories of "Erekose", "Hawkmoon", "Jeremiah Cornelius" and others, to get an entire understanding of it and what the character is all about.
Basically "Elric" was hated on when I was a kid the way "Drizzt" was hated on for a very long time (and still is to an extent), but in the case of "Elric" a lot of it seemed to come down to people who read his series in isolation and didn't really grasp the entire interwoven picture and what a decent character he actually was.
There are a lot of characters like that with me I suppose. I'm probably one of the few people that will tell you that I thought "Longshot" (Marvel Comics) was cool, along with a few other side characters like say "Blink" that never seemed to go anywhere or get the attention they deserved.
-
When it comes to "My Little Pony" I'll say I'm not a fan, but you can't be around fandom as much as I am without getting some knowledge of it. Especially seeing as I wound up reading a few of the creepypastas/shock stories attached to and thought they were darkly amusing.
From what I've seen "Rarity" isn't particularly unpopular, she seems to pretty much fill the same niche as "Angelica" from Rugrats... and is actually one of the more popular/depicted/quoted characters as a result.
As far as Emperess Celestria goes, I don't watch the show so I can't comment, but I've heard similar accusations. I'd point out that when it comes to the USA your dealing with a country that is very anti-monarchy as a founding principle and the idea of one person having that kind of undisputed power is touchy to say the least. The thing is that Celestria tends to use her power, and not always wisely, and is responsible for antagonizing a number of the characters in the show from that position. Compare her to say the typical Disney portrayal of royalty where typically a strong member of a monarchy is either disempowered and unable to act as a focus for the story (as per The Little Mermaid), evil as in the portrayal of the "evil queen" stereotype, or portrayed as being an ineffective buffoon who doesn't actually rule for the most part, making it a non factor, like the king in "Aladdin". There are exceptions, but understand that especially in children's entertainment a queen/emperess acting like one and screwing with people is a bit off putting and disturbing, which I think affects people's perceptions. Perhaps there have been other American characters like this that haven't gotten this reaction (and there probably have been over the years) but I think that's a big part of the problem with this one at least. I don't watch the show so I can't really break it down more than the general vibe I get from listening to other people.... being a good guy and attacking the bad guys at the end of the day, doesn't mean your a good ruler and not a jerk.