There's an app called jutda-helpdesk that uses Python's poplib and imaplib to process incoming emails.  You just have to have an account somewhere with POP3 or IMAP access.
This is adapted from their get_email.py:
def process_mail(mb):
    print "Processing: %s" % q
    if mb.email_box_type == 'pop3':
        if mb.email_box_ssl:
            if not mb.email_box_port: mb.email_box_port = 995
            server = poplib.POP3_SSL(mb.email_box_host, int(mb.email_box_port))
        else:
            if not mb.email_box_port: mb.email_box_port = 110
            server = poplib.POP3(mb.email_box_host, int(mb.email_box_port))
        server.getwelcome()
        server.user(mb.email_box_user)
        server.pass_(mb.email_box_pass)
        messagesInfo = server.list()[1]
        for msg in messagesInfo:
            msgNum = msg.split(" ")[0]
            msgSize = msg.split(" ")[1]
            full_message = "\n".join(server.retr(msgNum)[1])
            # Do something with the message
            server.dele(msgNum)
        server.quit()
    elif mb.email_box_type == 'imap':
        if mb.email_box_ssl:
            if not mb.email_box_port: mb.email_box_port = 993
            server = imaplib.IMAP4_SSL(mb.email_box_host, int(mb.email_box_port))
        else:
            if not mb.email_box_port: mb.email_box_port = 143
            server = imaplib.IMAP4(mb.email_box_host, int(mb.email_box_port))
        server.login(mb.email_box_user, mb.email_box_pass)
        server.select(mb.email_box_imap_folder)
        status, data = server.search(None, 'ALL')
        for num in data[0].split():
            status, data = server.fetch(num, '(RFC822)')
            full_message = data[0][1]
            # Do something with the message
            server.store(num, '+FLAGS', '\\Deleted')
        server.expunge()
        server.close()
        server.logout()
mb is just some object to store all the mail server info, the rest should be pretty clear.
You'll probably need to check the docs on poplib and imaplib to get specific parts of the message, but hopefully this is enough to get you going.