I have been pondering exactly the same issue and am struggling for an elegant solution. The thoughts I currently have are:
If the PC is always on it could be set up as a mail server - think that this is the IMAP option that has been mentioned, but it sounds complicated and I am not sure what software is available to do this at a reasonable cost - setting up a Microsoft Exchange server seems like overkill.
Use the auto forward option (if supported by the ISP) to forward all incoming emails to separate accounts (eg
[email protected];
[email protected] etc). Then each account can be downloaded to the relevant machine and all emails will be on that machine independently of the others. This does not require any machine to be always on, but only works for incoming mails, and they will appear as unread on each machine. To keep the sent boxes in line you could cc sent mails to each account or manually merge them periodically to keep them up to date - I believe that Outlook has this functionality.