I'm currently designing a website using HTML, and was wondering if it's possible to make the pages automatically center no matter what screen size it's being viewed on.

As an example, follow this link and resize the browser. You'll see what I mean.

I would like to stick with HTML if at all possible. Thanks!

I dropped by the Page and it is displaying "centrally" on my computer/browsers(IE7 & Chrome)@ Full Page
NOTE All browsers will distort text slightly if the Windows Frame is shrunk and Default settings is at this "Level"

The Webpages that may have issues (at full screen) are those with 3rd party images added which will distort the Page
Your Banners & fonts are all in Proportion

Sorry for the confusion... the site I linked to is not my page. That is just an example of how I'd like my page to look.

The table has a "center" align like this:
table width="760" border="0" align="center"

What software do you use to write the page? You could check the program's Help menu, table align section.
Hope this helps!
Dwight