The topic also begs the question, "What, exactly, is a BOARD game?"
But to give it a go, my first-line ten nominees, based on my own personal preferences, would include:
Cosmic Encounter
Illuminati!
Risk!
Battleship
Scrabble
Mouse Trap (and there was another Rube Goldberg-type game called "Crazy Clock")
Trivial Pursuit
one of my personal favorite word games:
Jotto
and these two true classics:
Backgammon
Chess
I've avoided mentioning home-versions of the classic television game shows:
Jeopardy!
Password, and
The X-Thousand Dollar Pyramid
And there's the new breed of classic:
Settlers of Catan
Ticket to Ride
Blokus
Bootleggers (a favorite which seems to be fading)
Do we count card games?
Magic: the Gathering
Dominion
and even Apples to Apples