Before I buy my next laptop, I'd like to make sure that it will work perfectly with Ubuntu. Is there a list of completely supported computers anywhere?
There is an ongoing QA effort for Laptops and Desktops in the Ubuntu Community - you can find that information here:
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.
Another retailer for preinstalled Ubuntu systems is ZaReason.
It's too general a question to make one specific recommendation so your best solution is to look at the Ubuntu Certified Hardware page.
You can review which laptop best suits your requirements by the manufacturer of your choice.
It lists all the laptops certified for Ubuntu by release as well
There is a wiki page of supported hardware, but I don't think it's fully exhaustive. The motherboard I'm using works fine and doesn't appear anywhere on that list.
There is an open hardware validation programme for laptops, desktops, and netbooks called Ubuntu Friendly. It is still under works, and will probably will launched for 11.10.
The launchpad project is located here
The idea is to allow anyone to test any hardware, and report the results back. Multiple positive results for the same hardware will result in a Ubuntu Friendly certification.