Yes! The Linode Backup Service is an add-on service that provides completely managed and automated backups, and includes three backup slots (nightly, weekly, monthly) plus a user definable snapshot. Monthly pricing for the backup service is $5/$7.50/$10/$15/$20/$40 for Linode 512/768/1024/1536/2048/4096 plans.
Even without the backup service you are protected against a hard drive failure on the host, as we utilize hardware RAID mirroring across multiple drives. However, this is not a substitute for proper backups.
If you have enough unallocated disk space on your account you can duplicate your disk images in the Linode Manager. It’s also simple to clone images between multiple Linodes using the Linode Manager.