I don’t know if there really ios a board game hall of fame (probably, there’s a hall of fame for everything). No matter, which games would say have to go in with the inital class?
For me these are the top of the heap
- Chess
- Monopoly
- Scrabble
I think “Risk” and “Axis & Allies” have to be on there.
I see you suffer from the same problem that King Arthur did in Monty Python and the Holy Grail.
I like your list and I would also include Risk.
To make it 5, I will take Clue.
Jim
Chutes and Ladders (though I’ve never played it)
Mystery Date, (just for the theme song alone)
Kill Doctor Lucky
For historical reasons, Parcheesi and Backgammon.
It may not be old enough , but Settlers of Catan should probably be added sometime. Also Puerto Rico (I’ve never played, but it ranks high on boardgamegeek.com)
Brian
And how could I forget Go? Probably the oldest board game still played.
Brian
Sorry!
Aggravation
Trivial Pursuit
Acquire
Life and for the little people, Candy Land.
Checkers
Hungry Hungry Hippos
Operation
Stratego
Battleship
Connect 4
Games Magazine has a Hall of Fame, though it’s not limited to board games.
(And would Operation, Hungry Hungry Hippos, and Connect Four technically be “board” games? Hmmmmm.)
Here are the games in Games Magazine’s Hall of Fame: Acquire, Axis & Allies, Blockhead, Bridgette, Civilization, Clue, Diplomacy, Dungeons & Dragons, Magic: The Gathering, Mille Bornes, Monopoly, Othello, Pente, Risk, Scrabble, Sorry, Stratego, Taboo, Tribond, Trivial Pursuit, Twister, Twixt, and Yahtzee. As you can see they do not include public domain games like chess or go.
Dogfight. From years ago
Spent many hour playing that game.
Backgammon
I just want to second, or third, Acquire. Great game. I read a comment once that it’s a crying shame that almost every household in the US (and in Britain, too) owns a copy of Monopoly, but relatively very few people have even heard of Acquire. It’s the great American boardgame.
Diplomacy.
Possibly the greatest board game ever.
Masterpiece, because it’s fun, the pictures are pretty, it teaches you how to estimate value and probability, and because it is incredibly cool to go to a museum and watch your ten-year-olds discuss Georgia O’Keefe, Caravaggio and Edward Hopper with the guide.
I also liked Careers, which struck me as a much more fun and jazzy game than Life. It’s all about the combination of fame, fortune and happiness, baby!
Does anyone remember Feudal? Here are some pics. I loved that game. It was like chess on crack. 
Mousetrap!
Rube Goldberg meets the boardgame. I loved that game.
Another candidate would be Chinese Checkers. In this age of political correctness would we have to change the name of this game to East Asian checkers?
My little sister had a Barbie boardgame that she loved. She would pester me for hours until I’d play this with her.
I’d also suggest the home versions of Jeopardy and Concentration should make your list.
I loved Feudal, I probably still have it somewhere. Few would play it though.