Actually this depends on the mail client you use. Outlook will store it in a temporary directory and delete along with the message.

Other mail clients such as Eudora physically download it into a directory. This may have changed since the version I was using given all the new breed of viruses (virii?)

However the general rule of using a good AV program and keeping the signatures up to date and making sure it checks your email as it is coming in will save you a whole log of headaches.