Monopoly is a bit of a classic. No one ever wants to play it though, takes too long. I really must buy my own board though, I mean if you don't have Monopoly who are you?!
In my family an old favourite is the London Game. The board is a Tube map (circa 1975) and you travel around on the different lines to visit tourist attractions. It's more versatile than most ordinary one-direction board games and also meant I had conclusively learnt how to get around London long before I ever actually visited it.
The one we play most often when I go home is Trivial Pursuit cos my family are kind of quiz nuts and we all like to prove we are more knowledgeable than each other.
I personally love Pictionary, Taboo and Balderdash but again others aren't so keen and you can't play by yourself
My best game is History of the World because I've only played it twice but I won crushing victories each time and now no one will play me again.
I got my bf a German board game for Christmas called Die Siedler von Catan. There is an English version of it (Settlers of Catan) but we thought nah we'll play it in German. We've had four days and not worked out the rules yet. Not so smart.