First off, this is not really for me, but for a customer.
The customer used to go to iGoogle, then click the Mail link. This brought them to GMail, where they sign in with their username@telus.net account into Google. That was their Google account, and GMail basically acted like an email program for them. Last Friday, GMail kept coming up saying that they need to create a GMail account to use GMail, and that would replace their account.
When I turned on the laptop and checked their browser history, it follows the story. Their @telus.net account is their username, no doubt. The password matches their Telus account for accessing Webmail, but it doesn't look like Telus is secretly forwarding to GMail. So my question is, is it possible to use GMail as an actual email client if you don't have a GMail address? If so, how can I enable it?

From <gmailuser>@gmail.com on behalf of <Senders Name> (<username>@telus.net)- but I don't think this can be avoided, unless perhaps you are using Google Apps as @Dave suggests? – w3d Oct 25 '11 at 19:12