While fine-tuning a technical workshop for next week, my co-presenter and I realized that our comment of "don't forget these knowledge base articles!" (see terminology note below) wasn't very helpful. You used to be able to go to http://support.esri.com and type in a knowledge base/technical article number like 23025. That would bring up "FAQ: Projection Basics: What the GIS Professional needs to know."
The Support website has been redesigned and that trick no longer works. Below I've included the new links to some of the useful coordinate systems, map projections, and geographic (datum) transformations technical articles.
23025: http://support.esri.com/technical-article/000005562