Asterisk, by Orange Range (Bleach OP 1)
Thank You!, by (I don't know the artist's name ;_

(Bleach ED 2)
Undo, by Cool Joke (FMA OP 3)
Rewrite, by Asian Kung-fu Generation (FMA OP 4)
Tobira no Mukou he, by Yellow Generation (FMA ED 2)
Kasabuta, by Hidenori Chiwata (Gash bell OP 1)
Kimi no Kono Koe ga Todokimasu Youni, by Takayoshi Tanimoto (Konjiki no Gash Bell OP 2)
Personal, by Ueto Aya (Gash Bell ED 1)
Stars~You don't have to worry about tommorow, by KING (Gash Bell ED 2)
Anna ni Issho Datta no ni, by See-Saw (Gundam SEED ED 1)
Ignited, by T.M. Revolution (SEED Destiny OP 1)
Pride, by High and Might Color (SEED Destiny OP 2)
The third SEED Destiny ending, by Yuta Nakano (don't know its proper name :<)
Reason, by Nami Tamaki (SEED Destiny ED 1)
Life Goes On, by Mika Arisaka (SEED Destiny ED 2)
Nazo, by Miho Komatsu(Detective Conan OP 3)
Unmei no Roulette Mawashite, by Zard (Detective Conan OP 4)
Truth~A Great Detective of Love, by Two-Mix (Detective Conan OP 5)
Giri Giri Chop, by B'z (Detective Conan OP 6)
Start, by Rina Aiuchi (Detective Conan OP...one of the later ones.)
Meikyuu no Lovers, by heath (Detective Conan ED 2)
Kimi ga Inai Natsu, by DEEN (Detective Conan ED 4)
DreamxDream, by Rina Aiuchi (ending to the 8th Detective Conan movie)
Kimi ga Ireba, by Iori (insert song in most/all the Detective Conan movies)
Believe, by Folder 5 (One Piece OP 2)
Bon Voyage, by Bon Bon Blanco (One Piece OP 4)
Glory -Kimi ga Iru Kara, by Uehara Takako (One Piece ED 7)
Ready Go, by Naomi Tamura (Pocket Mosnters OP 5)
Challenger, by Rika Matsumoto (Pokcet Monsters AG OP 2)
Battle Frontier, by Akina Takaya (Pocket Monsters AG OP 4)
Chiisaki Mono, by Hayashi Asuka (ending to 6th Pokemon movie)
Hohomi no Bakudan, by Mawatari Matsuko (The Yuyu Hakusho openings. All of them.)
Unbalance na Kiss wo Shite, by (don't know the artist for this one either :<) (YYH ED 3)
Butter-fly, by Wada Kouji (Digimon Adventure OP)
The Biggest Dreamer, by Wada Kouji (Digimon Tamers OP)
Bokura no Bouken, by Kids Alive (Hikaru no Go ED 1)
Close To Your Heart, by Rina Aiuchi (Monster Rancher OP 3)
There're a few songs that I left off of that, but the list is huge enough already :<