Listmania!
2 player games to play with a grade schooler
By an Amazon.com customer
Deluxe Wood MancalaDeluxe Wood Mancala
Fun, strategic play: yet a second grader could still beat you at it.  That's why ancient games have staying power.
BattleshipBattleship
Buy new: $34.59
One of those classic MB games:  if your kid is old enough to handle the markers, you're set to get sunk.
Rapid 4Rapid 4
A truly fun variation on the Connect Four idea.  You can play it mindlessly or strategically and enjoy it both ways.  And both ways, your kid could still win.
Connect FourConnect Four
Buy new: $26.49
S much better than basic Tic Tac Toe and its inevitable gridlock (or victory for the first player, once your kid learns that particular trick).
Blokus ClassicBlokus Classic
Buy new: $27.49
Award winner, and rightly so.  The two player version is longer and a tad more complicated than the 4 player version, but it's still playable and fun.  Worth it for the more "hardcore" among you.
Ravensburger LabyrinthRavensburger Labyrinth
Buy new: $25.59
This is one of my favorite games of all time:  play by yourself or with up to three more players, and the game is always different and challenging.  Very small kids may prefer the JR version.
OthelloOthello
Buy new: $19.99
This game is easy to learn, and even relatively small children can play it.  But it is much harder for them to win this one against adults, so be careful.
Hasbro OperationHasbro Operation
Buy new: $34.00
Basic skill game.  If your hands are as shaky as mine, your child may have the advantage. Try removing the rubber band instead of putting it in for younger players.
Milton Bradley Jenga Board GameMilton Bradley Jenga Board Game
Buy new: $19.95
Another skill game: cheap and fun.
Guess Who? Board GameGuess Who? Board Game
Buy new: $15.66
Thi is a great one for all ages and it helps vocabulary development. (try using rare adjective synonyms to describe features)