My site has several listing pages and on each page, I'd like to enable a commenting mechanism, but I want it to be as open source as humanly possible. This means full use of OpenID's, Facebook connect, etc. Does such a system exist that'll allow users to post their comments on my listing pages?
By the way, my site utilizes a LAMP architecture.
Your use of "open-source" is confusing in this context. Facebook Connect is closed-source, and OpenID isn't anything-source - it's a standard, and there are both open- and closed-source implementations of that standard.
You seem to mean simply "a wide variety of authentication methods". There are oodles of plugins for OpenID/Facebook/Twitter/etc. authentication on most of the major CMSes. If you want an all-in-one system, DISQUS is the best I've seen. It's a pretty simple JavaScript drop-in, and has an API for exporting comments into other systems like WordPress.
I had a similar question a few weeks back. Check it out, there are self-hosted and externally-hosted solutions.
Unobtrusive, self-hosted comments function to put onto existing web pages