My first thought would be that your mail is being intercepted by a spam filter but you have not provided much information about your ISP or how your email account(s) are set up. I have assumed we are talking POP.

There is nothing wrong with Mac OS X 10.3.9 or Mail.app that would cause such a problem.

Do you have more than one email address (not email alias)? If so, send your email to another email address and see if that turns up. If you don't have another email address then create one (Yahoo or Gmail) and check webmail to see if it is reaching there. Then set up to have it received in Mail.app and see if it turns up.

rgds,
centurion48