Strategery is a fun app that allows online play against other users. (Haven't done it myself yet but it's listed in the options.) It's sort of like a simplified version of Risk. Fun little app if you like those sorts of games.
I also have a combination bowling/shuffleboard game called 10 Pin Shuffle that allows you to play against another user head-to-head, but I get the sense that both of you need to be on the same WiFi network. Again, I haven't tested that part of the game out so I can't say for sure. But it's basically 3 games in one; shuffleboard, bowling, or a third game that is a mix of bowling & poker...you don't keep score, instead as you bowl you get 2 cards for every strike and 1 card for every spare and at the end of 10 frames you compare poker hands and whoever has the better poker hand wins. Very different game, adds a new twist to things.
Both of those apps are under $5, and each has a Lite version you can test out for free. Might be worth your time checking them out.