There are two approaches to solving the problem: Progressive Enhancement and Graceful Degradation.
This post will introduce both concepts (hopefully unbiasedly), with examples of both.
Another example is YouTube. They are trying to have all their videos viewable using HTML5 technologies. As a graceful degradation, if a user does not have a compatible browser, the video is displayed in flash. If you do not have flash installed, you get a polite message telling you to either download flash or upgrade your browser.