My list of anime would be much too long. I've got a list somewhere of at least 80 titles that I remembered the names of. Somewhere. I've been watching anime for nearly 20 years now. Many of them I didn't even know were anime until I was about 15 years old or so.
Some recent and not so recent titles I enjoyed. Some of these I may not remember much more than knowing I enjoyed them.
Sailor Moon, Oreimo, Clannad, Kanon 2006, Air TV, Yu Yu Hakusho, Cowboy Bebop, Shiki (Finished yesterday), Hellsing Ultimate, Gravitation, Abenobashi Shopping Arcade, Kare Kano, G Gundam, Gundam Wing, Dragon Ball, Great Teacher Onizuka, .hack//Sign, .hack//Legend of the Twilight, Big O, FMA: Brotherhood, Monster Rancher, Ronin Warriors, Ghost in the Shell, Samurai Champloo, Outlaw Star, Dai Mahou Touge, Sword Art Online, The Melancholy of Haruhi Suzumiya, Seitokai no Ichizon, The World God Only Knows, Sunday Without God.
Of these, favorites are Oreimo, Clannad, Yu Yu Hakusho, Cowboy Bebop, FMA: Brotherhood, Sword Art Online, Melancholy of Haruhi Suzumiya, Great Teacher Onizuka, TWGOK and Sunday Without God and S-Cry-Ed.