Here's a few suggestions for when you just want to sit down and have some fun with the family:
Tsuro is a very quick and easy game. It takes minutes to learn and can play with up to 8 people in about 15 minutes, and it doesn't take a lot of thought. Try to keep your stone on the board as you place paths and follow them. Watch out for the other players as their paths can force you off the board. Yes, players do get 'knocked out' of the game, but Tsuro is such a quick game, everyone will want another round.
Hey, That's My Fish! is another quick game, this time about moving penguins across an ice flow and picking the fish they land on. The trick is, picking up fish also removes a tile from the ice flow, leaving a 'hole', and the penguins can't cross holes, so the board gets smaller as the game continues. Hey, That's My Fish! is lots of fun, particularly for younger players. It plays up to 4 players and does take 5 minutes to set up the ice flow of tiles.
Fluxx is a very popular card game that can be played with any age. It starts with just two rules and as the cards are played, more rules are added (or taken away). After a while a 'goal' card will be played - and this gives players a chance to win. If you've got the right 'Keepers' out (Goal-Keepers, geddit?) you win. Hard-code board game players don't like Fluxx but that's because they miss the point: it's just plain fun!
Niagara is an unusual game in that the game box is part of the playing area. Take your canoe down the river to collect gems, but don't go too far and get dragged over the edge of the waterfall. Yes, there is some strategy here, but the game is just plain fun. Don't worry about going off the edge, you have two canoes and it costs a gem to get a 'lost' canoe back.
Cube Quest is a simple combat game of flicking cubes across the table at each other's army. If you're not careful, the cubes are going to fly everywhere, but that's part of the fun. It only occupies 2 players.