I have young kids and it's the Wii.
To be honest, it depends what the family would like to play. Wii games targeted at the family and it's platform style games are easy to pick up and good fun, even the grand parent enjoyed them.
I think a lot of these replies seem to have missed this part of the question
and family fun games not shoot em ups etc
It's also cheap at the moment new, balance board makes some games more enjoyable but not always needed (Raving Rabbids) and of course Wii Fit Plus always entertains my one's and myself and the wife even use it.
I'm sure the 360 with the Kinect feature and the games coming out for it will be great fun especially for the older family/kids. I've not had a chance to play though.
But more expensive.
ME as a gamer since late 80's