From what hasn't already been mentioned but I've played a lot on, games I enjoyed include:
Love Hina Advance - (All but complete english translation available! Great if you like the show).
Chocobo Land - Game De Dice (Fun board game with Chocobos ^^ )
Prince of Tennis games (Tennis no Ouji-sama) - best Tennis games on GBA after Mario Tennis.
Mermaid Melody - Bemani/DDR music game with full vocal tracks.
Azumanga Daioh Advance - Very simple card game with Azumanga sounds and images, but suprisingly addictive.
Dancing Sword - Side scrolling beat em up, hard as nails special moves will put some people off though.
DiGi Charat DigiCommunication - Fun shop sim game.
Mr. Driller Ace - Bit better than Mr Driller 2.
There are many other recommended games... I've heard good things about the Super Robot Taisen games and Black Matrix Zero for example.
Oh and check out this site for lots of info on Japanese GBA games:
http://jdb.pocketheaven.com/index.php
p.s Favourite Japanese game has to be F-Zero Climax... the new tracks and track editor are just awesome... Nintendo offer passwords/layouts for over 700 track designs (
link) and there's loads more out there not to mention your own creations too. It's crazy Nintendo havn't release it outside of Japan... it's miles better than the previous two GBA games.