Ok, i liked this thread
I assume that when you ask "only one hand" you mean you can't use the other hand to hold the Wiimote like an ordinary controller (sideways), am I correct?
I'm compiling the games from the previous answers, and adding some of my own:
Nunckuck Only - Confirmed (aka, I know they are)
Bit. Trip. Beat. (rithym game)
Bomberman Land (mini games)
Boom Blox (destroy blocks)
Broken Sword: Shadow of the Templars ~The Director's Cut~ (point-and-click adventure)
Harvey Birdman: Attorney at Law (a bit like Phoenix Wright)
Let's Tap (rithym game)
Professor Heinz Wolff's Gravity (puzzle like The Incredible Machine)
Marble Saga Kororinpa (marble madness)
Marble Saga Kororinpa 2 (marble madness)
Mario Party 8 (mini games)
Mercury Meltdown Revolution (marble madness)
Nights: Journey of Dreams ("flying" platform o.O)
Resident Evil Umbrella Chronicles (on-rails gun game)
Rockstar Games presents Table Tennis (ping-pong / table tennis)
Sam and Max Season 1 (point-and-click adventure)
Sega Superstars (tennis)
Super Monkey Ball: Banana Blitz (marble madness)
The House of the Dead 2 & 3 Return (on-rails gun game)
The House of the Dead Overkill (on-rails gun game)
We Cheer (cheering game. Although it's meant to be played with 2 wiimotes, you can play with only 1)
Wii Play (mini games)
Wii Sports (mini games - except boxing)
World of Goo (puzzle)
Zack and Wiki and the Quest for Barbados Treasure (point-and-click adventure)
Nunckuck Only - Unconfirmed (aka, I make no idea)
Art Style: Orbiant
Ghost Squad
Oopona (Said to use Nunchuck only...)
Mario Super Sluggers (soccer)
Anymore else? Anyone? Let's make this a compendium