If your incoming or sent messages are automatically placed in Trash, the cause is a misconfigured filter, or a setting on your Forwarding and POP/IMAP tab.
To resolve this issue, please make sure you haven't created any filters with the action Delete it that would affect the messages in question. If you have many filters or have complicated filters in place, you may need to edit the Delete it action to guarantee that they are not at fault.
If you've enabled forwarding in your settings, please ensure that you have not selected delete Gmail's copy in your forwarding options.
If you're using a POP client to access Gmail, please ensure that you have not selected delete Gmail's copy in step 2 of your POP download options.
Finally, if you're accessing your Gmail from multiple POP clients (with recent mode), please verify that you have selected 'Leave a copy of messages on server' in your client configuration settings.