Carcassonne has a nice iPad implementation as well. (As does Settlers--though it's a bit more complex and I find it's Carcassonne I come back to more regularly.)

I agree Carcassonne is a great gateway game. The basic rules are straightforward but there is some deeper strategy. There are also quite a few expansions that can add even more depth in different dimensions, so you can expand the game to your tastes.

Thank you for the suggestion.

Thank you for the suggestion. I tried to play this a few times on iPad, but not managed to have enoughtime play through. Will give it another try.