I have downstairs an old Dell Dimension from 2003. It wasn’t state of the art, not even back then. It is running a Pentium IV running at 2.8Ghz. My office machine, powered by a Core i7, is 15 times faster. So the question is, is it possible to make this machine still useful today and if so, how much and how much work would it take?
At the risk of starting a flamewar...
Install Linux on it. Seriously. Many Linux distributions have much lower requirements than Windows, and run just fine on old hardware. Especially if you use less demanding window manager like Xfce. It's not going to help for games because their requirements don't change, but for common tasks like browsing www, mail, word processors, playing music etc Linux will let you squeeze more out of aging hardware.
For a start I'd recommend burning an image of latest stable Ubuntu.
http://www.ubuntu.com/
You don't even have to install it, thanks to livecd. You can just insert the disk and boot into RAM, it won't even touch your HDD unless you tell it to. You can try it out (using some software, use the web...) before you commit yourself to any decision.
And if you want to squeeze the absolute max out of old hardware, there are distributions like DSL (Damn Small Linux; the image is 50 MB and fits even on small USB drives !).
http://www.damnsmalllinux.org/
Booting from USB is very convenient for many tasks, and it scares Microsoft. And if something scares Microsoft, it's good for the public.
http://blog.linuxtoday.com/blog/2009/03/if-it-scares-mi.html