What are the best current libraries/methods to authenticate users without the use of a CMS or heavy framework?
Responses should include suggestions for anything you
A lot of great answers here, but I feel like it's worth saying this--do NOT try to re-invent the wheel in this case! It is extremely easy to screw up user authentication in a wide variety of ways. Unless you really need a custom solution, and have a firm knowledge of security schemes and best practices, you will almost certainly have security flaws.
OpenID is great, or if you're going to roll your own, at least use an established library and follow the documentation!