All of your apps should work -- except those that need a Camera, or GPS. (GPS will work on iPad with 3G, but not WiFi only iPad)
If they are Universal apps, they'll have an iPad optimized UI with extra features, etc.
If they are standard apps, they will appear with a little (1x/2x) button in the corner, and you can zoom them to fill the screen. The UI will be the same as on your iPod Touch. Most games look great even in this mode. (Angry Birds, GeoDefense, etc.)
There are a lot of Universal Apps now, and more are being added all the time. There are 3 basic reasons:
1) The iPad is selling really well, so developers want to cash in on that growth.
2) With iPhone 4 Retina Display, all of the graphic assets need to be roughly the same size as the iPad. This means developers can create one set of high res graphics for both devices.
3) It is getting easier and easier to make a universal App. After the operating systems merge in November (everyone will be at iOS 4.2) you'll see even more Apps come out that way.