Elearning Guild 360 summarizes it:

Freeware LMS - Moodle is the most deployed and well-rated.

As for licensed LMS, I have lots of experience with systems, and really recommend:
1. Clearly define requirements (what you want system to do) and have vendors DEMONSTRATE how they do this during "shootouts"- of all the implementations I've been through, companies who stuck to this approach versus being "led" by vendor "features tour" were better off.
2. Trial, trial, trial
3. Have a defined timeline for success (e.g. 90d) and if vendor doesn't meet your criteria, write into your contract that you get it out of your organizations, costs recovered.

Any questions, please don't hesitate to ask. I have a copy of the 360 I could send you.