There isn't a way to get rid of them completely. With your Apple ID there is a complete purchase history of all you do through iTunes. You can hide them but they are still there. You can submit feedback to Apple that you would like to have an option to completely delete an app so it no longer shows on your account. http://www.apple.com/feedback/
Of course you also have the option of signing up for a new Apple ID but you would lose access to any paid apps under your current ID.