A Guide to K-12 Open Source LMS Options -- THE Journal
Overview of open source LMS options with examples of districts currently using them. This article covers Moodle, Sakai, Canvas, OLAT, ATutor, and Google CloudCourse. I thought CloudCourse was owned by Google, but it appears the code has an Apache license. CloudCourse seems to be mostly scheduling rather than a full-fledged LMS.
This is actually 18+ free and/or open source LMSs. Some are truly open source, some are freemium or other business models. If you want a list that goes well beyond Moodle and Canvas, this is a good place to start.