"The short answer to this question is "not much at
all." In fact, I don't think you could buy a computer at your local
Best Buy or online that can't run Linux.
"Let's take Ubuntu 9.04, which is due to arrive this week. The
official minimum requirements for this popular Linux distribution
are a 700MHz processor and 256MBs of RAM. I think that's too low.
In my experience, you could run GNOME 2.26 on that slow a
processor, but the RAM's way too low. You could pull it off with
512MBs, but you'd be happier with a Gigabyte.
"A reader recently claimed to me that he had an older PC that
can run Windows 7, but wasn't powerful enough to run any modern
desktop Linux. Yeah. Right. Windows 7 'officially' requires, a 1GHz
processor, 1GB of memory, 16GBs of free hard drive space and 128MB
of graphics memory on a chip set or card able to support DirectX 9.
As with every version of Windows going back to 1.02, Microsoft is
lying about the minimum requirements."