Can I allow users to login to two different sites using a single login?

Is there a way that my users can use the same login for two different sites?
I am not talking about multisite here. I know that'll work. I am talking about two different wordpress installations.
Not only do I want users to use the same credentials on both sites, but also automatically log in the person to both of them, when he logins to any one website.
Is this possible?