Not the parent but I'll chime in. It really depends on the type of games you enjoy. Mechanic-heavy ("eurogames") vs. more themed ("ameritrash"), cooperative, competitive, etc. BoardGameGeek is a great site for reference.

Off the top of my head, my wife and I enjoy: Ticket to Ride, Splendor, Ascension, Lost Cities, Settlers of Catan, Elder Sign.