SpiderOak - SpiderOak makes it possible for you to privately store, sync, share & access your data from everywhere.
imapsync - Console-based utility for migrating IMAP mailboxes.
Duplicati - Free backup software to store backups online with strong encryption. Works with FTP, SSH, WebDAV, OneDrive, Amazon S3, Google Drive and many others.
isync (mbsync) - mbsync is a command line application which synchronizes mailboxes.
CrashPlan - CrashPlan for Small Business backup software offers the best way to back up and store business & enterprise data securely - offsite, onsite & online in the Cloud.
MigrateCloudData IMAP Mail Backup Tool - A trusted software with better designs and functions to perform the backup and migration of IMAP emails.