Open-source would be good, but in the absence of all of that, I'm just going to use the stuff that comes with my Synology NAS:

• We keep valuable stuff (photos, etc.) directly on the NAS (using SMB).
• I can (but don't) use it as a TimeMachine destination. It can be a bit flaky -- it loses auth or something, but that can be resolved fairly easily.
• It's got some backup software on there that claims to be able to do agent-less backup of Linux and Windows servers.
• If you want to install an agent, it's got that too.
• It'll do backups to/from other Synology boxes.

All that said, I've not actually used anything other than backup-to-USB in anger. Other than "photos, etc.", I wouldn't be massively traumatised if I were to lose the data from any of my PCs. Because pretty much everything I do is in Github.

I guess I'd be annoyed if my/kids' Minecraft server was lost -- maybe I'll push that to the NAS as well.