It's a novel concept, but my family makes it a point to spend quality time together on a regular basis. These days people have so many activities that it is really easy for families to never be all together for any length of time, and when they do, all too often they are watching TV or something equally non-interactive.
One step in the right direction is to make it a point to eat dinner together and use it as an opportunity for meaningful conversation.
But our favorite thing to do is to play some kind of table game. I have always enjoyed games, and they provide a fun way to spend time together with an activity that encourages interaction. We like a lot of the classic table games, including various card games and board games, but there are also many lesser-known games which are a lot of fun. Here are a few that you ought to try.
Blokus -- Try to get as many of your pieces on the board as possible, with each one touching your own color only at the corners. Keeping your own options open while blocking off your opponents is key to the strategy.
Qwirkle -- Place different tiles in rows sharing a common color or shape. Complete a row of six to score a "Qwirkle" bonus.
Ticket to Ride -- Build a railroad network connecting key cities before your opponent buys up the routes.
Rat-a-tat-cat -- Silly name, great game requiring memory and strategy.