If you have checked the "Remember User Name" box on the Salesforce login page but your User Name is not, in fact, being saved, have your administrator take these steps:
Setup | Administration Setup | Security Controls | Session Settings | Check the "Enable caching and auto complete on login page" checkbox & Save.
Anyone in your organization who checks the "Remember User Name" box on the login page will now have their User Name saved.
This new session setting was released in our Spring '07 release. For new Orgs the setting was set "off" (unchecked) -- meaning auto-complete and caching aren't allowed. Any org in existence before the Spring '07 release had it set "on" (checked), to preserve existing behavior.
Also Note: Internet Explorer will not remember your Salesforce username despite having the above setting enabled for your org and selecting the preference on the login page. This is a limitation of the browser and not specific to Salesforce.
If you're not using Internet Explorer and the org preference above is enabled the issue may be specific to your browser.
Clearing your browser's cache and cookies and re-selecting the preference on the login page may resolve the issue. Please consult your browser's help documentation for intsructions on completely clearing all temporary internet files.
If the issue persists confirm that you're using our recommended browser settings however, please keep in mind the behavior may also be due to a setting outside of our recommendations such as a browser add-in that is inadvertently clearing the username.
Outside of these recommendations, Salesforce Support is unable to provide direct assistance with diagnosing browser specific issues that are external to the application's functionality.