This question sucks as there is really no favorite anime out there in the anime world because there is so much Animu, but I can list it down to two.
Cowboy Bebop - Great action. likable characters, and beautifully designed though it may be a tad bit outdated. It also blended the action with comedy perfectly with characters like Faye Valentine. Recently finished a few days ago and this is probably going to stand as my favorite action anime.
Azumanga Daioh - Everything about every episode is funny. This was done in earlier years before Lucky Star, Nichijou, or Toradora. It got a head start and all the characters are likable. The teachers, Chiyo-Chan, Osaka, Sakaki, Yomi, the works. It has a a great variety in comedy from the sexual perverted Kimura to the odd but funniest of all Osaka. Its an anime anyone can watch and enjoy all the way through. Best slice-of-life i've seen, plain and simple.