There are two ways to disable/remove your account. Its really very simple as I have done it once by myself too. If you're a Dropbox Pro subscriber, then you'll have to cancel out your subscription first. After doing that you simply go to dropbox.com/login?cont=https%3A//www.dropbox.com/account/delete and sign in. You will get remaining instructions there.
Also, deleting your account will delete your account from the website. Your computers will no longer sync with the website or to other computers or devices. However, canceling will not remove the files in the Dropbox folder on your hard drive or the hard drive of other members of shared folders you've created. Moreover, once I had many files of free TV
in my dropbox, I wanted to download them in my PC, but I forgot and remember that you can never get your account recovered.