Alright, I'll separate the list into two categories: Games that can be played without knowing Japanese and games that can't.
Games that require little-to-no Japanese or have been Fan Translated:
Tales of Innocence (Fan Translated)
Soma Bringer (Fan Translated)
Taiko no Tatsujin DS
Meccha! Taiko no Tatsujin DS: 7tsu no Shima no Daibouken
Taiko no Tatsujin DS: Dororon Yokai Daikessen
Vitamin Y
Osu! Tatakae! Ouendan!
Moeru Nekketsu Rhythm Damashii! Osu Tatakae Ouendan 2
SaGa 2: Hihou Densetsu: Goddess of Destiny (Fan Translated)
Okaeri! Chibi-Robo: Happy Richie Osouji!
Coropata (In the process of being Fan Translated)
Kaiju Busters
Tingle's Balloon Fight DS
Umihara Kawase Shun: Second Edition Kanzenban
Utacchi / Utatchi
Tokimeki Memorial Girl's Side: 1st Love (Fan Translated)
Games that cannot be played without knowing at least SOME Japanese:
Tales of Hearts
Nanashi no GAME
Nanashi no GAME ME
Love Plus
Love Plus +
SaGa 3: Jikuu no Hasha - Shadow or Light
Ace Attorney Investigations: Miles Edgeworth 2
Retro Game Challenge 2 (You may be able to play the games, but you won't know each of your goals without knowing Japanese)
Color Changing Tingle's Balloon Trip of Love
Blood of Bahamut