Kind of a wide open question, so I'll just name a few things that I find to be great.
PlayStation and Xbox SmartGlass, depending which consoles you use. Then there are game-specific apps for things like CoD, BF4, GTAV, etc.
Amazon and eBay apps are very well designed, especially the latter.
I can't remember if they come pre-installed now, but if not, you should have free access to download the Apple productivity apps: Pages, Numbers, Keynote, iMovie and GarageBand. The last two are particularly good.
And then there are all the games. Some of my favourites that work well on the iPad: SpaceChem, World of Goo, and Osmos.