You can change what happens when the inbox becomes full so old messages will automatically be deleted.
- In the user control panel switch to the private message tab.
- Click the link "Rules, folders & settings" on the left hand side.
- On the bottom next to "If folder is full:" select "Delete Old Messages"
- Use the submit button named "change"
You can make also make room by manually deleting old messages or moving them to a custom box. In addition to the Inbox you can have up to four additional boxes for grand total of 1000 message storage capacity. The custom boxes can be named whatever you want, for example you might want to create a "Saved" box to move important messages to if you're using the delete messages automatically.