These have all been important and influential to me. They are not presented in any particular order.
Sites and Blogs
Pubmed - Database of published medical research
The Cochrane Collaboration - International collaboration to review, rate and compile the published medical research
Quackwatch - The premier web source for information on questionable practices
Science Based Medicine - The premier blog for critically thinking doctors
The SkepDoc - Website for the writings of Harriet Hall, MD, skeptically-minded, retired doctor of Family Medicine
Respectful Insolence - Website for the writings of "Orac", skeptically-minded surgeon and researcher
White Coat Underground - Website for the writings of "PalMD", skeptically-minded internist and writer
Quackcast - Podcast on skeptical medicine by Mark Crislip, MD, skeptically-minded infectious disease specialist
Friends of Science in Medicine - Site committed to the maintaining scientific integrity within academic medical institutions
The Demon-Haunted World: Science as a Candle in the Dark - Carl Sagan's classic work. Considered one of the best intro's to skepticism.
Trick or Treatment: The Undeniable Facts about Alternative Medicine - Edzard Ernst, M.D. and Simon Singh comprehensively weigh the evidence
Taking the Medicine - Druin Burch's history of scientific medicine
The Panic Virus - Seth Mnookin looks at the history of the anti-vaccine movement
Autism's False Prophets: Bad Science, Risky Medicine, and the Search for a Cure - Paul Offit, M.D. explains the dangers of science and vaccine denial
Why People Believe Weird Things - Michael Shermer, Ph.D.
The Believing Brain - Michael Shermer, Ph.D. explains how our brains form ideas before we rationalize them
How to Lie with Statistics - The title says it all.
Nonsense: A Handbook of Logical Fallacies - Robert J. Gula, Ph.D. explains logical arguments and logical fallacies
Suffer the Children: Flaws, Foibles, Fallacies, and the Grave Shortcomings of Pediatric Practice - Peter Palmieri, M.D. exposes unscientific practices
Mistakes Were Made (But Not by Me): Why We Justify Foolish Beliefs, Bad Decisions, and Hurtful Acts - Tavris and Aronson explore cognitive dissonance
Nonsense on Stilts: How to Tell Science from Bunk - Massimo Pigliucci, Ph.D. looks at the fine line between science and pseudoscience
Thinking, Fast and Slow - Daniel Kahneman, Ph.D explores how our intuitive, fast-thinking subconsious informs our slower thinking conscious brain - (a MUST READ)
Distinguishing Science from Pseudoscience - An excellent essay by psychologist Barry L. Beyerstein