All the apps in the App Store will run on the iPad unmodified. You can run them in original size in the center of the screen, or press the 2X which gives you pixel double filling the screen. You can download all of your purchased apps directly on the iPad.
Also the developers can spend time modifying their apps to take full advantage of the display. In the App Store Apple will highlight the ones especially made for the iPad. Gameloft and EA already have special versions coming.
Games definitely look good on this interface, but text based apps, like facebook, do look a little awkward.
Images via [Engadget]