<h1>This is the example of fluid HTML</h1>
<p>Isn't that obvious: if you resize the browser window, this content is shown properly and remains readable for almost all sizes? Conclusion? Keep it simple…
This example demonstrates: if you keep everything simple, such problems don't exist. You create this problem by adding your styles, maybe even absolute positioning and other things. No wonder your layout cannot tolerate change in the browser window size. Pay attention that the screen size is not the only factor. The user can change the size of the browser window anytime.
It does not mean that keeping the design simple you cannot create good looking Web pages. This is actually a big art: Web design.
Among many other things, you may want to embrace liquid, fluid and elastic design
, all referenced to past answers: