It really depends on the fan I suppose, as each person has their individual tastes.
Just like with real people, everyone has type preferences.
I suppose my own tastes skew towards the more unconventional, but not so far field that it's too niche.
I like characters that are somewhat detached, who don't wear their heart on their sleeve, and when they do have an emotional outburst it leans more towards anger. They may or may not be monstrous in some aspect or another. They wouldn't be my ideal partner, they're not really husband/wife material. They're more the passionate fling that has an air of danger or trouble about them. It's a fantasy wish-fulfillment I guess.
For example: In the Dragon Age series, I thought Nathaniel Howe would have been a perfect love interest for my Warden Commander (except you couldn't romance anyone in Awakening). He struck all the marks that would make a good husband. Even-tempered, charming, considerate, I thought he was a bang up guy. BUT I wouldn't fangirl over him. Now FENRIS, yeah I'll go gaga over that. It was the first time I actually looked up walkthrough to ensure a romance with him after a couple failed attempts. I drew so much fanart of him … His romance is frustrating as all get out but dammit if I'm not a sucker for dark, broken characters. I could say the same for Robert Small in the game Dream Daddy.