I like all characters as long as they are protrayed in a way that makes sense with their character, I guess. The better question for me is what I don't like, which are characters that have a lot of plot armor that is so ridiculous unless ti's comedy because comedy isn't serious.

For male characters, I really like ones I find cute. I'm not exactly sure what the requirements for being cute are though. It's just something I feel when I see them. I also like dudes with pompadours.

For female characters, I like the ones with a more mature feel to them. Also the more androgynous ones like a lot of Riyoko Ikeda's females or Haruka/Sailor Uranus from Sailor Moon.

I really love main characters who are really shy or self-conscious and polite. I like them even more when they are super powerful 'cause it's just funny usually and then all the other characters are like 'Dude, tell us when something is wrong!' And the main characters just like 'it's nothing really!' but then main character is really suffering inside about some random issue. I don't really know why. That's why I LOVE Natsume Takashi from Natsume Yujinchou(Sorry if I spelled that last word wrong:3)

By far, I prefer characters that are mysterious, intelligent and unpredictable and also "grey", as in, not clearly good or bad. You can spend all the time in the world picking such characters apart, trying to guess their motivations or their next course of action.

I also love quirky and eccentric characters, stoic and deadpan characters and temperamental and badass ones. The most important thing is that the character must be fun to watch and preferably not too cliche.

I like cool and strong characters like Kaname from Vampire Knight and Byakuya from Bleach

and they must be handsome of course

I like characters that are sort of mysterious, hard to understand and to know. The ones that usually come off as rude or indifferent, not interested in social activities or keep to themselves.

OOHHH rant ahead! I've been analyzing my fav chara trends--

My favorite character types, in any and all types of media, mostly fall under the following categories, in order of most common to least common:

MALES:

1) Messed up dudes
Best description I can think of. >_> Jerks who secretly care but have too screwed up backstories to show it, slightly sad dudes who meet with tragic fates, totally loveable dorks who have questionable motives, all go under this category for me, which explains why it's hugetastic.
Examples include Ikuto from Shugo Chara, Anon from X-Note, Henry from Fire Emblem: Awakening, Elliot from Pandora Hearts, Kouichi from Digimon Frontier, Clive from Professor Layton, Hei from Darker than Black, Kida from Durarara, Ichiru from Vampire Knight

2) Smart dudes
They bring more intellectuality into their respective series and leave you thinking, while remaining geeks/nerds/dorks again. Earliest favie I remember that fits under this category is Yusuke Kazamatsuri from Genki Bakuhatsu Ganbaruger (Energy Bomb), but no one has watched that because it was only dubbed for my area and no one remembers it. For some reason, come to think of it, most of my favies from this category come from obscure fandoms (Konta Tsukino, Battle Bdaman; Clone Freud, Afterschool Charisma)
More notable examples include: Armin from Attack on Titan, Reid from Criminal Minds.

3) Main protagonists with a drop of tragedy
I normally do not like male protagonists because they're annoying (OMG I'M SO RECKLESS I'M GOING TO RUN INTO THIS BATTLE AND STAB THINGS BECAUSE I'M STUPID BUT I'M DOING IT FOR MY FRIENDS SO IT'S THE RIGHT THING TO DO!!11!1!!!11!), but the ones I do like usually have a sad little quirk that makes them loveable.
Examples include:
Ed Elric from Fullmetal Alchemist (He's a genius, yet he's made a lot of mistakes in the past, and his temper is adorable)
Allen Walker from D Gray Man (Because of Dark!Allen and his uncanny affinity for cheating in poker. Also all the shiet that happens to him. Seriously, poor kid.)
Rin Okumura from Blue Exorcist (Again, his recklessness and bad mouth actually brings about results he regrets, and they actually have a basis in the fact that he has demon blood. See also: awkwardness, periodical loss of self-confidence, ABILITY TO COOK)

And then there's Baccano. I love literally almost everyone in Baccano. >_>

FEMALES
I'm still not sure what it takes for me to have a favorite female character. I tend not to like females too much because they're often thrown in randomly as objects of romantic interest or just plain fanservice, and it's annoying. >_> I've noticed so far that my favorite ladies are weird as hell, badasses, or both. Hanji Zoe from Attack on Titan is a good example of that.

Uhhhh non-humans I guess? Let's see, I've liked Bass the edgy jerkass AI, Vash the cheery yet badass peacemaker secret plant thing, Death of Discworld who's totally chill, and the man-eating Parasytes. Also weirdly-shaped dogs and maybe normal-shaped dogs. So yeah, 90% of my faves aren't even human.