This site by Alan Kwan contains a lot of reviews of weird and wonderful Japanese games you don't ordinarily see in Europe or the US.

How about Kitty On Your Lap, "the dream game for players who like 2D anime-style cat-eared girls"?

Or Cotton 2: Magical Night Dreams, a shoot-em-up? "In Cotton 2, the player controls Cotton, a cute little girl and witch on a flying broom. (She has a mental age of 5, and thinks about nothing but food all day.) She is accompanied by Silk, a cute, scantily clothed fairy."

Or Chaos Seed? This is a game that involves cave excavation and attacks by villagers, and features Chinese mythology and even a functional Feng Shui game mechanism. It reminds me of Bullfrog's Dungeon Keeper, except the protagonist is not evil.