If you like hardcore point and lick puzzle games, Zack & Wiki is awesome. I don't know how overlooked the BIT.TRIP games are, but the first is one of my favorite games ever. Plus, the Wii actually got a physical retail release of all 6 in one package.

not sure if it qualifies as overlooked, but the de blob-series is awesome! great concept (seemingly ripped off by paper mario: color splash) and vibrant and colourful aesthetics (possibly a source of inspiration for splatoon)! de blob 2 has slightly improved controls and gameplay over the first game, so that's the one i'd recommend.

also i second little king's story and muramasa: the demon blade!

Boom Blox

Instead of using the Wiimote to shoot stuff... you use it to throw stuff :D

blast works is really fun, just one of those odd ones nobody will probably mention but it's a crazy game.

Definitely the Trauma Center games and Fragile Dreams. TC was a fun, challenging, and interesting type of series on the Wii that made good use of the wiimote and nunchuck. You can find this game for.... 2-3 dollars used. Def worth picking up. Fragile Dreams was an excellently made horror adventure game. The best part isn't its scary atmosphere, but the characters you meet. Interesting, strange, and endearing characters you encounter in this game. I don't know how much this goes for and I haven't seen it in stores since it was released, so... good luck getting this one.

Oh yea, Calling was a pretty good horror game, although not the lvls of Silent Hill 2 nor the FFrame series.

Project Zero 4
Silent Hill: Shattered Memories
Fragile Dreams
Deadly Creatures
Disaster: Day of Crisis
Lost in Shadow
Dead Space: Extraction
Ju-On
Night of Sacrifice
Captain Rainbow

Battalion Wars 2
Sin and Punishment Star Successor
Fire Emblem Radiant Dawn

Yeah, those were good fun. :)

A shame the studio behind them, Blue Tongue, went under shortly after releasing the second game. Australia's game industry got decimated last gen. :(

Tagging, I didn't play many Wii games but would like to see the recommendations

Fragile Dreams (wasn't a great game, but definitely good) and Muramasa are my two picks.