Horcrux lets you automatically backup your mails from any IMAP supported email accounts with great ease. The best part is, you have an option to restore the backed up emails to any other email account, retaining all your tags/folder hierarchy.

"Horcrux is handy since you don't actually have to think about it when it's running" - Lifehacker

Note: This is a background app, it resides on the Mac menu bar called "H". Click on that to get back to the preferences.

Features:
• Tested with iCloud, Gmail, Google Apps, Microsoft Exchange. It should work on most email accounts.
• Incremental backups
• Supports multiple email accounts
• Add the accounts, set the backup frequency and it'll unobtrusively backup emails in the background
• Native Email Browsing interface where you can undelete specific emails (in case of user error)
• Independent IMAP Server to Server migration utility
• Emails can be archived as a ZIP file making your data portable
• Clever restore process that'll skip already existing emails
• Stores emails in open format (.eml) which can be opened in clients like Apple Mail
• Can export emails in open format as .mbox

Requirements:
OS X 10.7+
64-bit Intel