ReplyToTicket
A user with the Reply'To'Ticket right can send Correspondence on a ticket.
This right is granted to the Everyone group in a new RT installation. Under most conditions it is necessary to grant this right to everyone, because otherwise an unprivileged user (e.g. external customer) that accidentally changes E-mail address would not be able to respond to questions on the ticket anymore. Admittedly there are risks associated with this.
Per this post on the rt-users mailing list, it may be best to grant this permission to Requestor instead of Everyone. -- Wohali
See also: Rights, GlobalRights