I’ve been playing Outwitters nonstop for about a week now. It’s turn by turn strategy where each player controls a team of beasties in an attempt to get to and destroy the other base. You can play with your wife taking turns on the same iPad or each using your own. It’s also got a really robust league system so you can play strangers and it will automatically match you with people of roughly your skill level.
There are three factions you can play with, each of which has seven units. Six of them are functionally the same, with the special unit varying from team to team in what it can do. The game comes free with one team, and that’s all you need to play forever, but you can buy additional teams. They’re cheap – currently $3 for the whole schmear.
A million times recommend Ticket to Ride. It’s not just one of the best board game ports on iOS, it’s one of the best games period. It has both LAN mode (if you each have an iPad) and a pass-and-play.
Really, iOS is great for implementations of many board games, and a lot of strategy/German/adult board games have gotten good ports. I also get a lot of play out of Puerto Rico and Tigris and Euphrates, though I haven’t tried playing them multiplayer. I’ve heard nothing but good things about the Carcassone app, but haven’t bought it.
The Awakening series is really good. Dreamless Castle, Moonfell Wood, Goblin Kingdom.
A very casual collect items and use them to solve puzzles game with a fairy tale story line.
Also, if you like something like bejeweled but more in depth gameplay 4 Elements is fun. You make jewel links to break away the space behind them allowing an element to flow through that space on a scrolling game screen to a predetermined goal before the timer runs out.