Of course, doing Web Design in the 'old' way will not disapear! However, the new concept called Responsive Web Design using the latest technologies in HTML5 and CSS3 open new possibilities. Complex Web Sites with lots of information are difficult to implement like shop systems and alike. But changing the thinking into 'less is more' could certainly allow lots of Web sites to fit this new concept.
Not all the functions so far defined in HTML5 and CSS3 are implemented in all Browsers but many of them are. No reason not to try them out! Using Grid Design to define the pixel positions, which will later be transformed to relative positions is very helpful. The next important item is to use the media queries to dynamically adopt the design layout to different screen sizes. It is a lot of hard work at least in the beginning! The books I already mentioned are extremely helpful. An interesting Site to visit to see that the new HTML5 and CSS3 can do is http://www.theexpressiveweb.com by Adobe Systems.
If I can help you with designing your Responsive Web Design Site just let me know!
Using HTML5 and CSS3
For Google and Bing
Supporting Web Sites
Some implementtations using HTML4 and CSS2.1
Working with other people...