I got to play an absolutely amazing board game last night. "Return to Dark Tower" is an absolute dream of a game.
The game itself has elements of the board games Pandemic, X-com, and Talisman.
It's this coop game where you wander around the board completing quests and cleansing corruption.
It's connected to this electronic tower and iPad app, but they make it work really really well.
In terms of app based games...
I didn't really like how Descent: Legends of the Dark felt like a video game that happened to have some board game pieces associated with it.
X-com did it pretty well, but used real-time play to keep the game speedy.
This one, I think, really gets it right. The app basically handles all of the complex work of the enemies and events, while you handle your cards and whatnot yourself.
To do this without an app, you'd need a ton of decks of cards to randomize enemy behaviors and events.
Basically, like an event deck, a dungeon deck, a deck for each monster, a deck for each companion, a deck for each villain, etc.
It'd be a lot of card draws and such that really wouldn't have a lot of value.
The app just does a lot of virtual card draws for you. In fact, many of the things are actually conceptual virtual cards, keeping the game grounded as a board game.