If you are subscribed to Dropbox Pro, you must cancel your subscription before deleting your account.
To delete your Dropbox account, visit https://www.dropbox.com/account/delete and sign in to your account using your username and password. Enter your password and select the reason why you are deleting your account from the drop-down menu. You may optionally give more details why you are deleting your account in the text field. Click on the button labeled “Delete my account” to delete your Dropbox account.
Be advised that although your account is deleted and your computer will no longer sync, you will have to manually delete your Dropbox folder from your computer.