Well, the standard Ubuntu version is growing with the current computers. If you want to run Ubuntu in an old computer, you can select another desktop environment, which you do by installing the lightweight flavour Xubuntu or the ultra-light-weight flavour Lubuntu.
If you have already installed Ubuntu, and don't want to reinstall, you can add the corresponding desktop(s)
and switch between them at the login screen. Click the round symbol according to the attached picture.
sudo apt-get install xubuntu-desktop
sudo apt-get install lubuntu-desktop
Edit: If you have problems with the newest version, you can also try some flavour, re-spin or distro based on Ubuntu 12.04 LTS with long time support.