Let's see....

"Kanashii Yokan" -- Tsukuyomi -Moon Phase-
"Pressentiment Triste" -- Tsukuyomi -Moon Phase-

(Technically, the two above songs are exactly the same, except one is in Japanese and the other in French.)

"Ningyo Hime" -- Chobits
"Raison D'etre" -- Chobits
"I Hear You Everywhere" -- Chobits
"Tenshi no Yubikiri" -- Kareshi Kanojo no Jijou (aka Kare Kano/His & Her Circumstances)
"Motteke! Serafuku" -- Lucky Star
"Tori no Uta" -- Air
"Panic" -- Kodomo no Omocha
"Neko Mimi Mode" -- Tsukuyomi -Moon Phase-
"Kinjirareta Asobi" -- Rozen Maiden
"Toumei Shelter" -- Rozen Maiden
"Bouken Desho Desho?" -- The Melancholy of Haruhi Suzumiya
"Lost My Music" -- The Melancholy of Haruhi Suzumiya
"God Knows..." -- The Melancholy of Haruhi Suzumiya

Just to name a few.