Jobs can be setup to automatically e-mail the job's owner when the job has completed. This is enabled on a job per job basis. A job is also allowed to e-mail a user besides the owner. This is specified in the job's addresses field.
Example
E-mail when the job is done.
% qbsub --flags mail ls
Email anon@server.com
% qbsub --flags mail --address anon@server.com ls