Most of the services redirect. Not all. 🙂
As you know, you can map Google apps core services to a subdomain such as mail.yourdomain.com or docs.yourdomain.com.
It's a great way for your users to easily reach them -and really, that's good enough.
There is no good reason for mail, calendar or docs to display your domain name after you arrive at the service. You aren't trying to make them rank higher in search engines and there really isn't an advantage to typing in a subfolder like mail.yourdomain.com/sent
Google sites is the exception -for good reason. You want your website pages to be found on the internet and rank in search engines.
Even on a free google apps account, you can map a google site you create to www and use Google sites as your main website. When you visit yourdomain.com you will arrive at your domain and it won't redirect somewhere else. You can also make other sites for intranet use with employee access and map them to a subdomain like reports.yourdomain.com or external sites like forums.yourdomain.com
On Google Apps, do you host the entire app on your domain, or just the login page?
