So I'm just starting to figure out the Apple Game Center. Anybody else play games like Neuroshima Hex or other board/strategy games?

Here are the games I have installed on my iPod Touch that are versions of existing board or card games:

Ascension: Chronicle of the Godslayer (Dominion-like card game)
Carcassonne (classic tile game)
Catan (classic trading game)
iDixit (award-winning party game - can't play it until I get an iPhone next year, but it was free for a limited time)
Ingenious (elegant board game)
Neuroshima Hex (tile-based wargame)
Ra (classic tile game)
Roll Through The Ages (combines Yahtzee and Civilization)
Tichu (cool trick-taking card games)
Uno (yes, it's mass-market - but it's still fun)
Zombie Dice (simple yet silly-fun dice game)

In addition, for strategy gamers, there are a few cool apps that aren't games per se:

7 Wonders Scorer - Score a game of 7 Wonders with or without expansion.
Agricalc - Score a game of Agricola.
BoardGameGeek - The app for the #1 board game website.
Dominion - Generates kingdom decks for Dominion, and also runs the Black Market deck.
Magic trading card game database - Self-explanatory.
MTGJudge - Also self-explanatory - rulings database.
Start Player - Very cool-fun app to choose a starting player.

My name on GameCenter is (go figure) GamerInterface.

There's also an app for Arkham Horror.

Carcassonne is a great pass-and-play game.

I'm going to have to look into Ascension, love that game.

Hey, somebody else has Catan on the iPad? Awesome! I'm getting pretty tired of playing against the AI.