We actually play board games every Sunday. My wife and I started it up with our daughter years ago for the purpose of teaching strategy and critical thinking. The weekly winner picks dinner the following Sunday. It's turned into a fun filled family murderfest every week. As a result, we have built up quite a large collection over the years. These are the ones we keep coming back to though.
PVP Games:
Ticket to ride
Cataan
Small World
Alhambra
Agricola
Sequence
Firefly
Libertalia
Dominion
Space Trucker
Robo Rally
The Red Dragon Inn
Munchkin
PVE Games:
Zombiecide
Mice and Mystics
Betrayal at House on the Hill
Pandemic