If you look at the hardware specs of the PS3 (on Wikipedia, for example), you will notice that the system has 256MB RAM and 256MB VRAM.
What is going on here? Is it the processor or is it something more that I'm missing? In my opinion, this is way too little compared with what good looking games need on PCs, for example.
Best Answer
As requested, I've converted my comment to an answer, and added a few more details:
More with less, but still less
An important thing to note is that consoles do relatively more (graphics-wise) with less (hardware-wise) than PCs due to lighter OSes and (usually) thorough optimization by game devs, but in the end gaming PCs have much more to work with than consoles do, so they do produce much better results than consoles.
Low-end PCs are still better than consoles
Even if you were to define "Gaming PCs" very broadly as "any PC with a low-to-mid-range graphics card made in the last few years and at least 2GB of RAM" (which means relatively cheap PCs still qualify), such a "Gaming PC" should be able to render games at higher resolutions and with more effects than consoles.
Consoles take shortcuts
The first way game developers get around the hardware limitations imposed by consoles is they make the console render the game at a lower resolution, and then upscale the images to fit the TV. For example, consoles run CoD4 at 1024x600 pixels with 2x anti-aliasing, which would be rather pathetic on a PC.
Here are some lists of actual PS3 game resolutions:
Beyond 3D forums - this seems to be where the upscaling was first noted and documented
Even more details from Beyond 3D - this is a more complete list of actual game resolutions/effects
Furthermore, consoles generally use lower-quality textures than are available in their PC-based versions, since they lack the RAM to load more detailed textures. Here's a good comparison of the textures Dragon Age, and here's a comparison of screen shots in Fallout3, Dead Space, CoD:WAW, and GTA4.