Travel Blokus is lots of fun. It's a really simple game to play but a hard one to master. The full sized game is much better for 4 players while this version is great for 2 players.

Mancala is a great game - it's probably one of the oldest board games in the world! Target had this game last year in their Vintage Game section - it was in a tin box, very nicely packaged. It's a great strategy game. http://www.tradgames.org.uk

You can't go wrong with scrabble!

Othello... simple enough that youth can play too, yet requires some thinking...

I used to play a lot of Cribbage with a good friend of mine when i was younger. Scrabble is fun too though. If you're into the German games (Settlers of Catan), Twilight Struggle is rated the top 2 player board game in that circle.

Depends . . . strategic thinking . . . skills? Pente and Othello are great games if you want to use your brain! Mancala is also a great game!

I would recommend backgammon. It is very strategic, and seems to only get more fun the more you learn about it.