Ubercart

If you browse to Administer > Store administration > Conditional actions, you'll see a list of all the "predicates" on the site that control what to do when certain things happen on the site... like what to do when a customer completes checkout. These are organized by these triggers by default, so just scroll down to the "Customer completes checkout" trigger listing and click the edit link for the "E-mail checkout notifications" predicate. From there you can go to the Actions tab to see what actions will be performed in this predicate. There is one fieldset for a customer checkout notification and one for an admin order notification. You'll want to expand the admin notification fieldset, make sure the settings are correct (like the admin e-mail), and save your changes.