CaptYamato said:
Anything and everything. Games would also suffice.
Games--be sure to check out the iOS thread on the Gaming Side. I think Rage HD is still free, and that should be a great deal. Infinity Blade and Real Racing 2 are also the major games that take advantage of the graphics capability. World of Goo and Plants vs. Zombies take advantage of the touchscreen well, Labyrinth 2 HD takes advantage of the gyros/accelerometer, and all those board games take advantage of the screen well. Then there are games in all sorts of genres--adventure games: Puzzle Agent 1&2, Monkey Island 1&2, and the Back to the Future games. The latest rhythm game that people like a lot is Groove Coaster. And there are the short games that are great for picking up and playing for a short time--Cut the Rope, Fruit Ninja, Flick Kick Football, Tiny Wings, Bumpy Road, Flight Control, Solipskier, and more. A lot of people like playing sim games (not me), which there are all those Kairosoft games, Civilization Revolution, and Tiny Tower.
Major apps: Kindle, Skype, Twitter, Pandora, Yelp, name-your-favorite-site, name-your-favorite-newspaper, name-your-favorite-magazine, and its ilk.
Your bank probably has an app for online banking.
Goodreader seems to be the go-to reader that most people use for document reading.
Bamboo Paper is good for note taking by hand/stylus. Adobe Ideas can get you there too.
Browsers: iCab is a Firefox-like browser, and Skyfire plays flash videos.
Language/foreign: iPad usually has great language-learning apps, just search the language. I also find it has a ton of apps geared toward non-USA stuff (example: basically all major Chinese portals, video streaming sites, etc. have a well done app) if that is something you're interested in.
Professional: Whatever profession you're in, there usually are some apps geared to that. From helping farmers to helping doctors.
Cookbooks: How to Cook Everything is probably the best, but I've got a lot of apps from those celebrity chefs, and I think Food Network, Betty Crocker, AllRecipes, BigOven, and Epicurious are free recipe repositories. The paid apps usually have photos, videos, and more in-depth instructions.
Sports--probably some good apps for any sports you follow.
Random: I use 1Password for all my passwords. Make sure to download and setup the "Find My iPhone" app which will let you track where your iPad is (if it's connected to the net) on a computer or an iPhone. You might just want to download the apps for the major sites you visit, and see if you think the app is a better experience than the website, and delete the app if not.