Testing with many browsers, and understanding how different factors can affect presentation, is crucial. Separating the concepts of markup and presentation will lead to better presentation in all browsers. Browser independence certainly means not relying on features of specific browsers, such as frames or marquees. Using such features is different from being dependent on them, and the key difference is whether the presentation still works if the feature is not available. It is also important to recognize when a feature may involve trade-offs, such as the amount of screen space taken up by frames, or the additional server delays they cause.
Browsers do vary a great deal.
Graphic support may not even be an option. Speaking machines may read pages to the user. Palmtops and WebTV involve restrictions that are unique to their environments. It is important to get readers to the information they want as quickly as possible. It's also important to remember that readers will look for different kinds of paths and navigational support, due to either situational aspects or personal preferences and working habits.