It sounds like you’re referring to what are known as “clean” or “friendly” URLs. I’m not aware of a way to do it at the root level of your site, but if having the pages at URL.com - Media Options (or some such) is acceptable, then there are a couple options.
One option is free and has been very well documented and described by @keith, and has been discussed in a number of forum threads. Search the forums for “gib/u” or “clean urls” or “friendly urls”.
Another option is the recently released Sudsy Page plugin. If you need more than one level of “depth” or would like the forward/back browser buttons to work as expected, it might be worth considering.