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If you are using a fluid-width design, the content will flow and fill the horizontal space. This can be a problem on short pages viewed full-screen on wide screens - it is important to consider what will happen to floated elements etc. if the page is horizontally stretched.
If you are using a fixed-width design (usually at less than 800px) then it will only fill a very small part of the screen real estate when viewed on a high definition wide screen. This problem is mitigated by the fact that the vast majority of wide screen users will not have their browser window stretched full width.