I love all types of characters, so I guess my favourite type of character is one that is interesting to watch, especially when dealing with hardships.
I especially like characters who have shit thrown at them 24/7 and deal with said shit in their own interesting ways. I'll throw in a few examples:
Guts from Berserk. His life is absolute turd from the very start, and he's surrounded by danger since birth, but the bastard just doesn't die. Many people in his position would have eventually broken down and given up, but he just keeps going, which I think is both interesting and awe-inspiring.
Kaneki Ken from Tokyo Ghoul is also a character that has to deal with a lot of shit. Because he's suddenly been placed in a position where he doesn't belong, he's forced to make drastic changes to his character, treading on the line between decency and unadulterated psychosis. He's an interesting watch, as he's constantly changing both in character and philosophical ideals.
And last but not least, Punpun from Oyasumi Punpun. Now, Punpun's hardships aren't as dramatic as the rest, but they're relatable due to its realistic setting and generally subtle tone. Punpun's hardships aren't immediate, but rather they build up and affect his psyche, which only breaks him down bit by bit until he turns into a complete sociopath.
I just realized that the characters I listed are borderline insane, so I guess that's my favourite type of character - the ones whose limits as the measly humans are pushed to, and maybe even past their boundaries, and watching them break down and build themselves up again.