This page has links to various live demos. So instead of having to remember all the cool demos we have you can just go here. Many of these are _not_ production or guaranteed to be up. For the best list of those go to http://opengeo.org/gallery
First thing to point out is that we have screencasts of some of these, at http://presentations.opengeo.org/screencasts/foss4g/
You should download those so you can show things off even when offline.
Production / Clients
(more at http://opengeo.org/gallery)