Our kids are too young yet to play video games, but I think family games on the Wii could be lots of fun in the future particuarly on rainy days, or days when you need to get out of the sun. I think playing as a family is preferable to kids spending too long inside playing alone on video games.
I don't have kids, but when I was one, and even now, my dad will still play with me. I have a Wii at the moment, but used to play a lot of platform and racing games with him on the PS1/2. I'm now becoming less interested in video consoles, and have started playing on tablets, so family gaming is becoming more rare.