Any 700c (622mm) tire will fit on a 700c rim, but there are combinations that work better than others. For instance, a very narrow tire might not span well across a very wide rim. Likewise a very narrrow rim won't support a very wide tire. There's a tire/rim compatibility chart near the bottom of this page:
http://www.sheldonbrown.com/tire-sizing.html
It's fairly conservative, so going slightly outside the recommended choices will be okay. (Rim width is measured on the inside.)