Ticket to Ride, Carcassonne, NS Hex, Battle of the Bulge, Agricola, Does Not Commute, This War Of Mine, Spider 2, Tiny Wings, Prune, etc. etc. I've bought 100-200 games, many of them very good.
XCom and Pandemic are the ones that I've spent the most time on. The iPad is a fantastic form factor for board games, and XCom worked better IMHO on iPad than on console or PC.
There's http://www.metacritic.com/game/ios for recommendations. Works well. That said, discovery on the App Store is simply atrocious. Absolutely terrible and a complete embarrassment for Apple since the start. Even recommending games to me that I already own!
Puzzle Games: