Have your users run the jobs with a workflow. Per-tool, in the right panel where job configuration is set up, there is an option to send an email once the job completes. The email is sent to the registered user's email address.
With the right email settings (in whatever client you are using), should you be running the job/workflow, you can set it up so that these emails forward.
Or, share or publish the workflow (and possibly a history with the inputs - or put these into a public Data library) then have the user's run the workflow themselves. As admin, you can always go into their accounts and take a look at thier contents for troubleshooting/help/feedback (Admin > Impersonate a user).
Hope this helps! Jen, Galaxy team