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The minimum system requirements haven't changed much over the years. 9,04 Jaunty Jackalope uses a minimum of 256MB. Ubuntu with it's own flavors can be ran on anything from a 939 AMD to the newest of the newest processors.
When upgrading my wifes laptop how ever she got an error that, for her older laptop, the graphics driver wasn't available and desktop effect might not work. However, the generic driver works just fine. The effects are not going to be missed by her anyway.
The Update from 8.04 to 9.04 went by remarkably fast only 10 minutes.
For more read the release notes you will find more important information on what might or might not work in the new version there.