Thunderbird is your desktop client that can archive, compress, and store all emails offline. I've even used Thunderbird for migrating all my email history, folders etc. between servers: simply add new account and drag and drop folders between accounts. Simple enough to be used by non technical people who do not want to: >./imapgrab.py -d -v -f ~/user@email.com -s imap.mail.server -S -p 993 -u user@email.com -p passwo…
Be careful using Thunderbird to move mail between IMAP4 servers, on Linux at least - I've had it lose messages on me, deleting them from the source before they're successfully written to the destination. I was moving mail from a Gmail account to a Gandi account about a year ago, before the recent spurt of development activity on Thunderbird.
Always copy, verify that the messages really are at the destination, then delete. I don't know why this isn't what Thunderbird does on its own when you move mail, but it isn't.