To delete Dropbox account is very easy, you only need to follow the removal link :
STEP 1: OPEN THE REMOVAL LINK
STEP 2: ENTER YOUR EMAIL AND PASSWORD TO LOG IN
STEP 3: ENTER YOUR PASSWORD
and indicate a reason for leaving Dropbox. You can then click Delete my account when you’re ready.
Your account has successfully been removed. You’ll see a confirmation of it.
Source screenshots (& thanks to): Dropbox.com