Free learning material I'm aware of several excellent youtube channels that are free and provide some great insight into the game, such as:


Chess Network
Online Chess Lessons
ChessFriends.com
Kings Crusher
Mato Jelic
YM Chess Master (IM Andrew Martin)


What are a few other good resources (free only please!) that a new player can find and how can I use them effectively to improve?
Here are some sites that I have found to be of great value:

chessopenings.com - NM Dereque Kelley explains openings very well.

The Chess Website - Excellent videos.

ChessVideos.tv - An abundant resource of top notch videos.

Exeter Chess Club coaching section - Excellent articles

ChessCafe columns (especially Dan Heisman's Novice Nook columns and Mark Dvoretsky's Instructor columns) - I can't recommend Dan Heisman enough,  his videos on ICC (not free) are excellent. Note: since the demise of the ChessCafe site these links point to the archive.org saved version.

50 Chess Games for Beginners - I stumbled upon this. Looks helpful, especially since the games are annotated.

Chess Visualization Training - Improve your visualization.