I'm a Linux guy. My media library lives on spinning rust drives in my NAS. The original CDs/DVDs/Blu-Rays etc. are one backup, a copy on a USB HDD serves as another. Most personal files on my computer are synched to my laptop and/or phone via Syncthing. This isn't strictly speaking a "backup" but it is a redundancy that can survive some failures. I back up my desktop nightly via BackInTime (a front-end for rsync) to one of three external USB hard disks. I cycle through these drives weekly, the freshest one goes to my parents' house as an offsite backup (I store his off-site backups as well). Applications and Software, I use a tool provided by my distro which essentially keeps a list of the installed packages, which can then be bulk-installed by my distros package manager. I don't really bother trying to archive my applications or take full image backups of my system because I've found just doing a fresh install and then restoring a backup isn't much slower or more complicated.

ALL of my backups are done locally. I use no cloud services, and those hard drives me and my father swap as off-site backups are transported physically.