Things I use all the time, but not all may apply to you:
Facebook
Twitter
Netflix
DirecTV / HBO to go / MAX to go
PBS
Words with Friends
Flipboard
How to Cook Everything
I also have lots of reading related apps - Overdrive for library books, Instapaper, Washington Post, Kindle, iBooks, etc. That is what I mainly use my iPad for.
As for removing something, that would depend on what app you have it on. Usually most have a way to delete something - an "edit" button when you're looking at a list of books, a swipe feature that brings up a "delete" choice, etc. If not, things can be removed when the iPad is connected to the computer, using iTunes.