I have BackBlaze for multiple computers. They have no storage limit for each computer, however you need to understand the limitations. It is only intended to backup your user files, the system and applications folder are not backed up. There are also many file types that are ignored by default (like installers and virtual machines), but you can over-ride most of that.
It will also backup any external disks connected to the computer, but if a drive is disconnected for awhile (a month?) then the backup of that drive will be deleted (you get a bunch of warnings before that happens). For an additional charge, they will save those backups forever though.