My favorite anime? Hard to pick... I mainly like Type A (Story driven) anime, but the weirder Type B (Character Driven) anime are fun, too. I typically don't like harem or fan service series that much, unless it has a really, really good story.
Some of my favorites over the years were Slayers (スレイヤーズ), Dennou Coil (電脳コイル), Record of Lodoss War (ロードス島戦記), Kyōran Kazoku Nikki (狂乱家族日記), Toriko (トリコ), Neon Genesis Evangelion (新世紀エヴァンゲリオン), Fullmetal Alchemist (鋼の錬金術師), Bleach (ブリーチ), and One Piece (ワンピース). There are, of course, many more, but these are the ones that I thought of off the top of my head.