Sounds like you're using a POP3 mail client on the desktop. This is (or at least was) a common issue with Blackberry users using Gmail. The problem stems from the fact that the native Gmail message storage is seperate from the message storage that your POP3 client retrieves from, and that Gmail adds EVERY message this hits the native storage to the POP3 storage - including messages you send.
With Blackberries, the fix is to filter these messages on RIMs servers, so they don't get pushed to the client. So I think the only fix would be to somehow filter them using your own mail client. How/if you can do that would depend on which client you're using.
Another option would be to consider setting up your mail client to use IMAP instead of POP3. Since you would be accessing the native message storage, you probably wouldn't have the same problem.
I'm sure there are some disadvantages to going with IMAP, so you might want to look into that a little further before jumping right in.