I'm a new father that loves gaming in all forms, though I gave up video games just before my son was born (playing board games online doesn't count does it?). Over the past year I have formed a game group with a couple of other husbands to play longer epic style games like Game of Thrones (which I love) and Eclipse (meh). We also throw in Lords of Waterdeeep (great) and one of my new favorite Glory to Rome.
Despite the biweekly game group the vast majority of my gaming is with my wife and occasionally other couples. My wife loves games with lots of interaction, if she can't cause harm to what I'm doing she isn't happy. She also likes to see the game fold out in front of her, so tile laying and track laying games tend to be hits. She also really likes 7 Wonders with two players so she can use the city to steal every card I would want to use. As much as I've tried, she still refuses to co-ops, reasoning she plays to win and doesn't want to share the glory. Since we don't have as much time as we used to card based games that feature a tableau have been going over quite well.
Since I have limited time for gaming with groups I tend to play a fair amount of games solo, Lord of the Rings and Mage Knight being the two I play the most, though Mage Knight rarely sees the table now that my son is a bit more active due to its set up and play length. We just gave our kitchen a complete makeover, so I love having other couples over for dinner, and once the wine starts flowing I tend to break out the games.
In short winners tend to involve interaction, with my gaming group being fairly ameritrashy then my wife and I being cut throat euro. I am also a fan of games that have expansions, because I love variety.