I'm terrible with favorites, since I like things for different reasons, but I'll give you some recommendations.
Anything Miyazaki, mostly Howl's Moving Castle and Spirited Away
Mamoru Hosoda's film: The Girl Who Leapt Through Time, Summer Wars, Wolf Children (These films will rip your heart out)
Full Metal Alchemist Brotherhood, Shounen (Follows the manga beautifully and the animation is fantastic)
Soul Eater, Shounen (Same as FMA)
Gurren Lagann, Shounen (Beautiful animation and a touching story)
Planetes, Seinen (You need to get through the first 12 episodes, but then really gets good!)
Neon Genesis Evangelion, Shounen? Seinen? (A classic)
Chrono Crusade, shounen? (very short manga dealing with demons and exorcists and such)
Bride's Story, Yosei (Slice of life and BEAUTIFUL drawings. Deals with life in the old middle east area seen from womens' point of view)
Fruits Basket, Shoujo (Slice of life, heartwarming and fun, a most read I think)
Alive - The Final Evolution, Seinen (A fascinating read about guilt and suicide, also great style)
Ouran High School Host Club, Shoujo (Another most read/ classic I find)
Full Metal Alchemist, Shounen (Even though Brotherhood is a near perfect substitute, it doesn't capture the author's brilliant humour)
These are all finished stories, so no need to wait for updates.