Where can I find a list of computers guaranteed to work with Ubuntu?

There is an ongoing QA effort for Laptops and Desktops in the Ubuntu Community - you can find that information here:

Old Ubuntu Laptop Reports and for everything 11.04 and onwards, Laptop Testing Site

You can find the reports for Lucid tested Laptops tests here: 10.04 Lucid Laptop Tests. The best course of action is to find a handful of laptops you're interested in then check the Reports on each.

If you feel compelled to help you can find more information at the Laptop Testing page.

Finally there is a detailed list of compatible systems on the Ubuntu Certification page.

This page on ubuntu.com has the breakdown of certified machines by manufacturer and model type.

If you get a computer with Ubuntu preinstalled, it's guaranteed to work with Ubuntu. Dell and System76 are the two most recommended companies from which to get Ubuntu computers.