Oh man, so many anime to chose from. My all time favorite is Code Geass hands down, but Kill la Kill has really clawed its way into my heart and strangely enough helped me through some very hard times. (Don't lose your way has practically become my life motto.)
I usually am not one to hate on characters types/tropes, but I REALLY hate when a character gets crippled by something, and then act like "I CANT DO ANY THING EVER AGAIN I AM WEAK" and then suddenly something magical/science happens that makes them all better and they can do stuff again. Thats why I like Ayase Shinomiya from Guilty Crown. She cant walk, dose she act like its the end of the world? NOPE she rocks out in a mech! But thats more of a pet peeve of mine I guess.
I also hate "Mr Perfect" characters. Not to be confused with "Plot armor", I get plot armor. Some characters are important to the plot and require it to allow the story to continue. Mr Perfect's are like Yusie from Yugioh 5Ds. He didn't lose a single game on camera, any time he WOULD lose, something happened to interrupt the match. He was flawless, Mr Goodguy, never lost his cool, and was all around a snoozefest of a character.
I think my "favorite' character is probably Blackstar from Souleater, now THATS a character who legitimately grows as the story goes on. He starts out an annoying little welp, and by the end of things hes learned enough about himself and others to actually be a great character. (Ive noticed in most anime, the side characters always tend to do that more then the main character.) I mean Look at Attack on Titan, an anime I love. The main character is so... Eh, but all the side cast are AWESOME!