Depends on the game. Obviously Wii Sports yes, but even NSMB Wii. You have to shake the Wiimote to get the bubbled character close to a teammate. I probably don't need it for that but if Dad doesn't wear it then the kids won't and I don't want any "collateral damage"
Absolutely, 100% of the time I'm holding the remote (unless its like picking a song in Rock Band or something, and then I'm playing Guitar a minute later).