barackrocksall,

It sounds like you have a POP3 or IMAP connection with Outlook 2003. By default POP only pulls the Inbox. If you are using IMAP you can subscribe to subfolders, such as your sent items folder in order to see them in your Outlook client.

The only true way to see all subfolders is to set up your Outlook client with an Exchange connection (usually RPC over HTTP). In this case you would sync everything, but only if your information is on an Exchange Server that you have an account with. If not you will have to export a PST file of all your information and import it into your Outlook client so that it would sync up to the new Server. Unfortunately, you can only export and import PST files from Outlook and not Webmail...so hopefully it's the same account.

Let me know how you've configured your client, whether Pop, IMAP, etc. and what type of server your mail is on so I can give you a clearer answer.