i've had an iPad 2 for a about a year now, and, through the dizzying ocean of mostly terrible apps, just a few have stood the test of time:
Dolphin browser - an excellent alternative to Safari. For iOs, it's proven itself to be generally more functional than Opera and Chrome
Tunein radio - excellent little app for streaming radio. And it plays in the background!
IZip - unzip utility and pdf reader
Netflix - Netflix.
Only three game apps have survived:
Chess.com - best interface and most populated servers for playing free chess. No two ways about it.
Frotz - allows you to play interactive fiction games. More can be downloaded from ifdb.tads.org. If IF is your thing, there's a ton of content here.
Powder - a roguelike designed specifically for the gameboy advance. It ports nicely to iOs, and has, by far, the most ergonomic controls of any roguelike I've played on an iPad. There's a great deal more complexity in this game than you might have ever expected to find in any iOs game.
Other than that, the iPad, for me, is primarily a casual browsing/youtube machine that can't run Flash.