Well anything you might be interested in or use normally, could be anything.Thanks. What kind of productivity apps are you referring to? Any specific suggestions?
I don't use my iPad for work, at all. It's just a web browsing / email / iOS game machine for at home
If you need access to your computer for whatever reasons there's remote desktop and SSH apps along with a few network file browsers.
Screwing around with the various music stuff can be fun, Tap DJ (an iPhone app) is cheap and can potentially be hilarious if you just record random conversation with it (there's also djay which has better quality sound but doesn't seem to have mic recording). The Korg apps are all pretty nice, if confusing to get into (figuring them out is kind of a game in itself), there's a bunch of other stuff like that out there.
I use SketchBook Pro for drawing and more recently got TouchDraw to mess with vector drawing.
Back to games, King of Dragon Pass is kind of wacky and pretty awesome if you can get into it. It's iPhone right now but there's a universal iPad update in the works, and it's on sale currently. If you like puzzle stuff, SpellTower and Async Corp are nice (latter is iPhone only but it doesn't really matter).