Motionworks recently posted sage advice in Learning After Effects for Beginners, which collects some good resources to learn AE.
Another resource is Adobe itself, which provides some great free resources like After Effects Help and Support and Adobe.TV (see Timesavers and How To, for example).
Adobe.TV can be slow and difficult to use, but AE Help czar Todd Kopriva has an Adobe AE Help page Services, downloads, extras, and video tutorials, which organizes a master list of AE video tutorials (including ones from the CS3 era) from Adobe and partners into categories forming a comprehensive introductory "course." And this page is available in 6 languages!
Resources can be spread out across the web and hard to find quickly for a newcomer -- like good free video teasers from After Effects Apprentice by Chris & Trish Meyer that are tucked away in one of two PVC blogs and on Focal Press along with some other free content.
While still just a sampling, an overview of AE community resources before the Twitter craze can be found in AEP's own After Effects Online Resource Roundup and in the AEP News sidebars to the right.
Update: Mike Jones adds a few more basic links from book publishers, and "if you're craving a deeper consideration of the aesthetic and conceptual paradigms After Effects represents then I can thoroughly recommend Lev Manovich's essay After Effects and the Velvet Revolution" (who refers to a nice history of motion graphics by Matt Frantz).