My wife and I play Rumikub...well, she plays and I try to figure out why I lose so much. I have found the perfect mind numbing time user during this equally numbing time, hand painting with a double coat the 6ft high flat boarded fence that surrounds my property. It has sat paintless, exposed to all weather, for fifteen years and the wood sucks in the paint with an almost audible gasp. I have one side gate left to paint and that will require me to open the eighth gallon of white paint. It has been one of those jobs you can't wait to start and then wish you hadn't.
My wife and I enjoy co-operative board games as we are both competitive and don't like playing against each other.
One of our favorite games is called "Pandemic". Timley, I know. It is tough to beat but very fun and rewarding. We also like most of the "Cthulu" games like "Arkham Horror" and the like.
As far as competitive games we like the "Red Dragon Inn". This game is fun with at least 3 people.
Have fun and see if you can find co-operative games at your local game store.