You can easily rent DVDs on Netflix without the hassle of late fees, and many movies are even available for online viewing. With such ease of access, it makes sense that your "movie history" or "recently watched" lists will get overwhelmingly long. Technically speaking, you can't delete the lists, but you can delete your account and start a new one to clear your movie history.
Click on the tab that says "Your Account & Help" in the upper right-hand corner of your screen.
Click the blue tab on the middle right that says "Cancel membership" and follow the directions to finish closing the account.
Go to the Netflix main page and set up a new account. Creating a new account will give you a fresh history page, but all of your other preferences will also be reset.