Although the published minimum requirement of Ubuntu is pretty low, tests show that it's not practical to run Ubuntu linux on hardware which is too old, or just meet the minimum requirement. A better option would be "Lubuntu".
I've tested installing Ubuntu 11.10 on a laptop with Pentium 4, 1.6GHz CPU, 512MB RAM and 40GB HDD. Installation successful, however, the resulting performance is so bad that it's not practical for actual use.
Then, I noticed another edition of Ubuntu - Lubuntu, the light edition of Ubuntu. It takes much less resources, so even on a slower laptop like the above, it's still good enough. Installation is pretty fast. Hardware side, drivers were all successfully installed without any problem, not much difference from Ubuntu. Software side, basic web browsing, email, media player, word processor, terminal are all available inside the install ISO. Indeed, the desktop look is not bad, even better than Ubuntu (my personal opinion)!!
However, users of Lubuntu need to aware that besides the system installation, 3rd party application installation will not be as straight forward as Ubuntu. The Software Center is missing. In many cases, you will need to open a terminal, type commands to install software. Language pack support may cause you some difficulties. No office application is available by default, so more complicated word processing, spreadsheet, presentation features are not readily available, unless you install them afterwards.
Of course, Lubuntu is not as feature-rich and user friendly as Ubuntu, though it's a very good option for computers with slow CPU and lacking RAM. A computer with Pentium 4, 2GHz or lower, or 512MB RAM or lower, Lubuntu should be your choice.
Those who have interest to try it, here's the official download site: