Although in the FAQ’s they claim there should be a deletion link somewhere, we couldn’t find it.
According to Curse, there is some kind of “problem” with the link, so you have to file a ticket to have your account deleted.
Go to http://curse.cursesupport.com/tickets/new and select the appropriate option (for a free account, “delete non-premium account”.
Please note that AccountKiller.com is not associated with the business listed on this page. AccountKiller provides easy-to-understand instructions and guides on how to cancel charges and relationships from the list of businesses on our site, we have no affiliation with these businesses.