Let's step back and define "run".
Most systems from the last say 2-3 can run a newer game at acceptable frame rates, etc basically at a medium setting depending on your system. Sometimes all you need to do is pop out a video card and pop in a new one every few years. RAM is inexpensive as well.
Now, to run some games as high as it can go can be out of reach of all but those who tweak and spend $500 on a video card.
Also, keep in mind there are MANY, MANY more games with decent graphics and a lot of playability available to a PC with average prices running from $9.99 to $20 rather than the almost default $40 range for a 360/PS3 game.