Jobs can be setup to automatically e-mail the job's owner when the job has completed. This is enabled on a per-job basis. It is also possible to send e-mail to any other address. This is specified in the job's address field. Emails are sent from the Supervisor, so it must have that ability enabled.
Examples
E-mail job owner when the job is done.
% qbsub --flags mail ls
Email anon@server.com
% qbsub --flags mail --address anon@server.com ls