offlineimap is a nice tool to synchronize your IMAP accounts with local mail folders. By using offlineimap you’ll be able to have your e-mail locally in your computer for offline reading and also it will always be available on your IMAP server for when you don’t have your computer at hand (i.e. you can still use a webmail interface).
Just follow the instructions in offlineimap’s manual. You can use a configuration similar to the following:
[Account zen3]
localrepository = Zen3Local
remoterepository = Zen3Remote[Repository Zen3Local]
type = Maildir
localfolders = ~/Maildir.zen3[Repository Zen3Remote]
type = IMAP
remotehost = mail.zen3.net
remoteuser = YOURUSERNAME@zen3.net
remotepass = YOURPASSWORD
ssl = yes