You can remove apps...except the apps Apple gives you, i.e., Contacts, Calendar, Email. As described earlier, when you press on an app long enough for it to wiggle...press the x and the app is gone. (Apple's given apps will not display the x--you can move these apps around, but you cannot remove.) That is step One.
Step Two, go to the Apps app and remove them from your app list. This will give you a warning and ask you: Are you sure? If you are then press yes.
I used to do this when I first got my iPad. But then I had no way of remembering which app I had bought and found useless. So I created a reject folder and put all unwanted apps into that folder. I also thought that I would prevent an app from updating but then I discovered that after some updates, some apps became useful!
YMMv!