Walker Boys Studio’s Free Unity Video Tutorials
Unity is one of the major free game engines available right now, and probably the best-suited to 2D as well as being perfectly capable of handling 3D.
Walker Boys has (have?) put together a massive collection of Unity tutorials, from introductions to the program and scripting to tools creation to a whole host of different ways to build different kinds of games.
The tutorials are incredibly thorough and typically broken down into small, single-topic increments, which helps keep them from getting intimidating or hard to find the answer to specific questions. Each series also includes any relevant downloads.
(This was originally sent to me by Ben Sutherland. Thanks Ben!)