From Bioinformatics.Org Wiki
A great place to start, whether you come from a biological, physical or computational background is at Martin Vingron's superb online bioinformatics tutorial. (Begin by choosing a section from the left-hand-side menu bar.)
Tom Smith and Don Emmeluth have produced a nice little exploration of bioinformatics using NCBI resources and tools.
I recently stumbled upon a promising set of online lecture notes currently under construction by B. Steipe at the Genzentrum (Gene Center) at the Ludwig-Maximilians-Universität München (University of Munich).
Chemistry for all
A defiantly frames-free chemistry tutorial site.
Mathematics for biologists
First of all, an almost completely painless introduction to the horrors of the quadratic equation by Peter Whalen, James Walker, and Drew Marticorena.
Computers for biologists
Programming for biologists
General introduction to biology for computer scientists
Estrella Mountain Community College in the States offers this excellent short introduction to biology (actually "The Nature of Science and Biology". It's a great place for keyboard jockeys to start their journey to enlightenment. Thanks to Alex O'Neill for pointing out the broken link.
The Dolan DNA Learning Center at Cold Spring Harbor has an outstanding interactive tutorial introducing genetics. To take full advantage of the multimedia elements you should download the Flash and Real players.
Molecular biology for computer scientists
The Institute of Arable Crop Research Beginner's Guide to Molecular Biology
Protein chemistry for computer scientists
Unilever Education Advanced Series tutorial on proteins.
Cell biology for computer scientists
The University of Arizona has made available a high-quality tutorial in cell biology. Not only does it cover the facts, but it also attempts to introduce some of the philosophy of the field---recommended. Even better, it's also available en Español and in Italiano.
Evolution for computer scientists
Bob Patterson maintains his "Darwiniana" with amazing diligence.