Scarlett O' Hara may be the classic "unlikable" but interesting character who is not actually a murdering psychopath. She did all sorts of awful things (stole her sister's husband, manipulated people, exploited prison laborers, was indifferent, even cruel, towards 2/3 of her kids, and so on), spent most of the book obsessed with a man she couldn't have, and she was a flaming racist too (though the biggest flaw of that book was how unexamined that aspect of her personality was, compared to the others--an example of how an author's core values will tend to creep in).
But she had a relatable goal, so the reader ends up rooting for her, or at least understanding why she did the things she did.
And even more unlikable characters, trending towards the murdering psychopath end of the spectrum, would be the ones found in many grimdark fantasy novels. In fact, with that genre, if you start liking one of the characters, even think that he's got a core of decency or is on a redemption arc, he will definitely do something completely beyond the pale in the next scene or chapter.
People seem to vary greatly in their taste for these sorts of stories. I find them intriguing because they can make me root for someone who has no moral compass at all, or whose moral compass is (by my assessment) completely broken. But I find they get tedious for the some reason that tales of unremitting heroism and nobility do--their predictability. And in some cases, it starts to feel like the author has to keep one-upping the shock factor, until it becomes almost a parody of itself.
And in the end, I generally read in order to see the character accomplish something meaningful and to share some emotional experience I can relate to. Life sucks and is often unfair. When I read, I generally want to escape to a world where the little guy can make a difference and where people can salvage some love and happiness, even in dreadful situations.
I'd say likable characters are more common in contemporary fiction and fantasy, and most especially in children's stories. But likable doesn't mean they don't have flaws or make mistakes. A character who is unremittingly good (Polyanna made me want to puke) is just, ergh. Many of the most memorable and likable character have a bit of vinegar in them. Some of the best-loved children's books characters were the kids who weren't goody two shoes, though they were basically decent. Ramona and Tom Sawyer both come to mind (examples from completely different eras).