I think there’s enough open architecture in the Facebook API that would allow someone to create a Gmail/Hotmail/Yahoo! Mail/Zimbra copycat. The current Facebook mail/messaging is very simple (no BCC, no forwarding, no quick access to your contacts).
You would need to have your own domain that you open up as the “free” email address domain (i.e. ‘fmail.com’ — stick away from ‘facebook’ being in the name, because that is copyrighted and FB may sue you in the future).
This app would tap into your FB network first as your main contacts; it’d allow you to import contacts from your Gmail/Hotmail/Outlook/etc contacts.
It would monetize via contextual ads like Gmail.
The user could use the app within FB or you could also have a stand-alone website.
You could integrate/create IM within the web-based app as I mentioned as a previous idea (although my previous idea was IM as a desktop app).
You can add a profile action link under every friend’s profile that says, “email this user”. Attachments are already built-in. Users could email to FB friends or email addresses.
You could also create a desktop app or AIR/Silverlight app using FB’s desktop API features — thus, you could create a MS Outlook competitor.
Big money in email, of course.