Supported Hardware List
To start I should admit that I haven't done much work in Ubuntu in a few years.
I am wondering is if there is still a single, canonical source of the hardware supported by the newest distribution of Ubuntu.
In specific, I want to get a 17-inch HP dv7t Quad edition laptop.
But more generally, it is just bothering me how little luck I'm having finding an up-to-date support listing.
The link to Ubuntu Friendly in the accepted answer is broken because the Ubuntu Friendly website was decommissioned five years ago. The official Ubuntu certified hardware information is currently available at Certified hardware | Ubuntu.
As of April 23, 2018, the link in this answer is no longer functional. It has been left in-place here for historical reasons.
Have a look at Ubuntu Friendly, though it isn't complete. Nothing beats testing computers with a live USB before buying. My recent experience has been that major incompatibilities are rare these days, though you might have to do a bit of work on some machines.