A private key corresponds to a single "identity" for a given user, whatever that means to you. If, to you, an "identity" is a single person, or a single person on a single machine, or perhaps a single instance of an application running on a single machine. The level of granularity is up to you.
As far as security is concerned, you don't compromise your key in any way by using it to log in on a machine (as you would by using a password), so having separate keys for separate destinations doesn't make you any more safe from an authentication/security perspective.
Though having the same key authorized for multiple machines does prove that the same key-holder has access to both machines from a forensic perspective. Typically that's not an issue, but it's worth pointing out.
Also, the more places a single key is authorized, the more valuable that key becomes. If that key gets compromised, more targets are put at risk.
Also, the more places the private key is stored (say, your work computer, your laptop, and your backup storage, for example), the more places there are for an attacker to go to grab a copy. So that's worth considering as well.
As for universally-applicable guidelines on how to run your security: there are none. The more additional security you add, the more convenience you give up. The one piece of advice I can give categorically is this: keep your private key encrypted. The added security there is pretty significant.