Cloud backups are great to have until you find out they haven't been running.
Local backups are great to have until the same power surge or fire, theft, water damage, etc., knocks out all the equipment.
Many people make this an "either/or" choice. Why? Why not have the reliability and speed of a local backup (Time Machine for Mac, Backup and Restore for Windows) and the location independence and redundancy of a cloud-based backup from services like Carbonite, iCloud, OneDrive and others?
Recreating lost files is either difficult or impossible, and the stress just isn't worth it. You may only need your backup once in your life, but you'll be so thankful you had it.
Local backup only is not a good idea.
Cloud backup only is relying on an external service that you "hope" is working.
Cover yourself with dual methods of backup. Put another one in a safe deposit box every year. Our lives now have far too much critical information in digital format to trust a single spot for such a dense amount of information.