What happens to my web based email (i.e. Gmail, Yahoo) username after I completely close down my account? Is the username I closed down made available to new users or is it retired for good?
In case of Gmail it depends on how you delete it.
Google support writes about possibilities of regaining your username depending on how you have deleted your account.
Therefore, it seems that your username won't be available for others to use in any case.
For Yahoo, when you terminate your account, the ID might be reassigned.
In most cases your account will be deactivated and then deleted from our user registration database in approximately 90 days. This delay is necessary to discourage users from engaging in fraudulent activity. Additionally, due to the limited number of names available, we may allow other users to sign up for and use your current Yahoo! ID and profile names after your account has been deleted.
The detailed procedure can be found on Yahoo's "How to close your Yahoo! account" help page.