Older kids here - we like Scrabble, Settlers of Catan, Carcassone, Mousetrap, Apples to Apples. For Settlers and Carcassone, we tend to use cooperative strategies rather than competitive - to be honest, I can't recall if this is part of the original rules or our variation! The kids like Life, but I don't.
Set is a favourite card game. They also like poker, euchre and cribbage. For some reason, crib is just not my game, so I rarely play it.
My kids are still too young for most games, but we enjoy:
Apples to Apples