Current gen only, since people seem to think that the current gen niche game no longer exists:
A puzzle-adventure game about a man and his dog with a sort of cut-out / pastiche Monty Python art style.
Use the controller to tilt, rotate, or flip levels and navigate your character through a Spelunker-style maze to get keys to unlock doors and find treasure. Extensive leaderboards and time attack / score attack options.
A twitch reflex puzzler; rotate the discs to make sure the falling symbols get through. Manic at the later stages. Cute presentation.
One part Ikaruga meets one part Snake. Oh, yeah, and you play as two different ships; one with each hand.
Kinda like Power Stone or another arena top-down brawler, wrapped in a presentation that's involves electoral subterfuge in the animal kingdom, fake news broadcasts, etc.
Katamari meets Nickelodeon cartoon art style.
(Bonsai Barber, WiiWare)
Every day, give five haircuts to fruit and vegetables. It's cool, because every day you only play for 15 minutes, but there's enough content to keep you coming back for a year; 64 haircut types, 15 or so different customers, an in-game achievement system, etc.
Paper Mario / echochrome style game that focuses on collapsing a 3d world into 2d puzzle mechanics. Very hard.
Dumb Nintendo fans keep clamoring for Pokemon Snap, but this is a hundred times the game Pokemon Snap was, particularly if you have an interest in photography. Extensive in-game photo options.
Not a particularly good atmospheric survival horror game. Ugly, lame controls, kinda low budget.
A very competent God of War / DMC-styled action brawler. Where you play as a scorpion or a tarantula.
Best light gun shooter I've ever played, love the RPG-style level up unlock system.
future tapping game
Katamari as a 2.5d game. Not based on Lunchables.
Half-way between Cooking Mama and Root Beer Tapper. Final stage is an awesome Iron Chef parody. Comes with a chef's hat.
I love trivia games. This is no exception.
DS really has enough for its own post, so I'll just leave with those four consoles.