Here are some games that are good and exclusive to Japan.
DoDonPachi (better looking and more close to the arcade version than the Saturn port)
Gradius Gaiden (best Gradius game - yes I prefer it over V)
Gunners Heaven (like Gunstar Heroes)
Gussun Paradise (Bubble Bobble style game)
Harmful Park (cute style shoot em up - but seem to be expensive now)
Money Idol Exchanger (aka Money Puzzle Exchanger - like Magical Drop)
Panzer Bandit (like Guardian Heroes)
Raiden DX (best Raiden game of original franchise - blends classic Raiden play with score base elements of the Fighters series)
Rakugaki Showtime (its like Poy Poy… on crack!)
Vib Ribbon (music platformer)
Zanac X Zanac (Compile's last game
also has the original versions of Zanac)
These are some games that are great fun to play and only available in Japan region.