I am a self-taught web designer, but then again, so are most. I have always had an interest in graphic arts, so the internet allowed me to explore the possibilities of a career in design. The books I initially used were from the Lynda Weinman series. She and her staff have created quite a library of web design texts and videos. Her website, lynda.com, has some excellent resources, although you'll have to pay for the good stuff.
Until a couple years ago, I made sure that any new site that I was working on displayed properly in every browser I could find. With a re-launch of bassbone.com two years ago, I decided I couldn't worry about software released in 1997 anymore. If you are operating Netscape 4 or Explorer 5, please do yourself a favor and upgrade today.
Much has changed since I began designing sites half a decade ago. No longer do I rely on embedded tables and pixel shims to create layouts. Now, CSS controls all aspects of my web presentations. XHTML is once again used only for page structure and content. These books will help you understand the importance of valid CSS and XHTML and their roles in designing web pages.
Below are a list of some of the sites that I use to stay up on the ever-changing web world.