I like charicters who has reasonable skil or talent, but arn't over powered.
Generaly I prefer wiscracks to moping charicter, emotional growth is good, but some charicters take the weak and vunrable personality too far.

Yuri Lowell is a good example. Skilled swordsman, glib and some personal growth.

The Casshern and Karas types.
The Goku and Vegeta kinds, as well.

I usually like the the characters that were weak in the beginning and grew thoughout the series to overcome the struggles and hard ships and become strong. I usually find characters that are always strong usually boring as you usually know what will happen in a fight.

Characters I have enjoyed:
Naruto - Naruto
Shu - Guilty Crown
Yoshino - Blast of Tempest
Hakaze - Blast of Tempest
Shizuku - My Little Monster
Hachiman - SNAFU
Yukino - SNAFU
Lelouch - Code Geass
Zwei - Phantom
Kira - Gundam Seed
Mikasa - Attack on Titan
Eren - Attack on Titan
Levi - Attack on Titan
Satellizer - Freezing

To be honest, it will usually depend on the story since it's not usually a single type on protagonist, its how the protagonist fits in the story for me.

I like protagonists whose roles as protagonists themselves are in jeopardy- as in protagonists like Araragi Koyomi and Hikigaya Hachiman, who can both be "replaced" by almost any other character around them.