I'll be updating this regularly, so check back regularly.
Beginners:
Jeff Galloway's Site. See also his books Galloway's Book on Running
Runner's World Need something? You'll probably find it here.
Competitive/Marathons:
Hal Higdon Training from the 5K to the marathon.
Competitor.com Tips, tricks and training ideas.
Running Times It's like Runner's World, but without the phrases "New Year New You!" or "Your First (or Fastest) 5K!" (also without forums)
Ultra Running:
Kevin Sayers' Ultrnr web site: Want to run ultras? Go here first!
Stan Jenson's Run 100s: Go long. Real long.
IrunFar.com Bryon Powell's blog with the latest news, interviews and gear reviews. See also Bryon's book, Relentless Forward Progress: A Guide to Running Ultramarathons
UltraMarathonRunning.com - Training resources for your next Ultra Marathon
Ultrarunningpodcast.com - incredibly informative interviews that are certain to help you get through you're next ultramarathon.
Minimalist/Barefoot Running:
Barefoot Running University Jason Robillard's blog
Runner's World Barefoot Forum
Running and Rambling - not necessarily a how-to but Donald posts frequently about minimalist running and minimalist shoes that are out there.
Books:
Marathon: You Can Do It!
Ultramarathon Man: Confessions of an All-Night Runner
Racing Weight: How to Get Lean for Peak Performance
RUN: The Mind-Body Method of Running by Feel
Daniels' Running Formula - 2nd Edition
Magazines:
Outside
Running Times
Trail Runner
Retailers:
Road Runner Sports
Holabird Sports
Eastern Mountain Sports
Finish Line
Newton Running
REI