I dunno about the JRPG thing man. Sure alot of the crap we've gotten has been horrible but there were lots that also broke away from the average storyline. You should try playing Valkyrie Profile 1 and 2 as it deals with Norse mythology. Ar Tonelico is also another unique game with unique storyline and gameplay, not the old school turn based at all. Demon's Souls is another JRPG with western flavor that doesn't hold your hand and is very niche with a more unique way of telling a story. Even Final Fantasy 8 was different from traditional final fantasies, the whole academy training you to be a mercenary part was appealing.
Platformers, hmm Ratchet and Clank actually fall into the platformer category except you shoot with some amazingly crazy weapons, loads of action and no, it's not collecting stupid coins and stars, you are probably singling out Nintendo's super milked Mario franchise, or Sega's Sonic.
I agree with Xen on the Rhythm games though. I am also getting sick of FPS', this gen has been more than saturated by them. ODST=ripoff for the consumer. Halo 3, MW1, MW2, Haze, KZ2, COD:WAW, BF:BC, Resistance 1, resistance 2, bioshock, etc, etc, etc,etc
And plz define minigames, because I see those as 85% of the games the Wii has gotten.