Τhis is my list of favourite anime IN ORDER. I've watched more anime of course, but these are the ones that have left me a big impression. The list starts from my favourite anime. I love every anime listed in that list.

Steins;Gate
Fullmetal Alchemist: Brotherhood
Higurashi no Naku Koro ni (Kai is included)
Gintama (all seasons included)
Kara no Kyoukai Movie 5: Mujun Rasen (all movies included)
Spice and Wolf (both seasons)
Mirai Nikki
Tengen Toppa Gurren Lagann
The Melancholy of Haruhi Suzumiya (both seasons + movie_
ef - a tale of melodies (memories too, but not as good as melodies)
Ano Hi Mita Hana no Namae o Boku-tachi wa Mada Shiranai.
One Piece
ERASED (aka Boku Dake ga Inai Machi)
Kaiji (both season)
InuYasha: The Final Act
Bleach
Sayonara Zetsubou Sensei (all seasons)
Evangelion: 2.0 You Can (Not) Advance (it would have been higher if the series ending wasn't that weak)
Sora no Otoshimono (only the two seasons, not the movies)
Nichijou
Lucky Star