joshhunt's answer is correct, but the "Deauthorize all accounts" link only appears if you have reached the maximum number of authorized devices (5).
I'm personally pretty picky about having an authorized device being that laptop that crashed 4 years ago and impossible to manually deauthorize singularly, but unfortunately, thats the way it is. An extremely long and unnecessary solution would be to set up a WinXP virtual machine, clone it a few times, then authorize all of them to the maximum your account would allow, then deauthorize them all, reauthorizing only the machines you use. But like I said, thats a lot of work for something that isn't necessary. Its best to let it be until the point you run out of authorizations, then fix the problem.
Regarding backups, those are tied to the account, not the machine. It is possible to restore a backup to a machine you aren't currently authorized with, but in the process, you will end up authorizing it with your account.