Is this user a mobile user?
If so, definitely have the user archive some of his e-mails to a local PST file. When the user disconnects from the Exchange server and the OST syncs, the sync time will get longer and longer with the more messages you have in the mailbox, especially over a modem line.
Assuming the user is local. . .
Exchange gets a little finicky when the mailbox size gets large. I would suggest having the user archive any e-mail over 30 days old to a PST file. You could setup the PST file local to his HDD or to a share on a file server. Just make sure it's going someplace where you are backing it up on a regular basis.
You can set up automatic archiving to occur from within Outlook. You can even make it automatic to the point that the user doesn't know it's happening (caution: you may get a phone call asking how come e-mail is missing).
Basically, whatever e-mails the user needs to have access to through OWA need to be stored on the Exchange server. Anything else can go to a PST.
You might also try having the user create a few subfolders off their inbox.
Hope this helps.