It's certainly a good idea, but probably not as important as offsite backups. Personally, I never bother doing full system backups. I just backup the files I will want to have if I have to reinstall the OS. An external HDD is certainly useful, but can be stolen, dropped, flooded, etc along with my computer.
My university gives each student 25 GB of Google Drive space, as well as 1 GB of space on an SSH server. I encrypt all my research related data locally and send it to both of those. Documents, PDFs, etc don't generally take up too much space.