To say that any old cable will work is not strictly true. If a cable is badly shielded, the signal heading down the cable might be affected by outside interference so much that you would get breakup or complete loss of signal on the output.
Also, I'm not sure what the spec is for HDMI, but any signal (digital or analogue) is going to degrade over distance, so you might have problems with really long cables. If you wanted to get the HDMI signal over cable which is longer than the recommended distances, you would need some sort of line driver to get the signal further. However I'm not quite sure how many are available in the domestic market, but most people will have their PS3, Blu-ray player or whatever under their TV so this is hardly ever a problem.
All said though, it's true that most cheap cables seem to be up to spec and are not excessively long so you'll find most are fine.
I have had an odd problem though which I believe is more to do with my monitor more than anything. My PS3 connects to my monitor through HDMI, and with some HDMI cables you'll get a better picture over others. When I say better picture, I don't mean better colours or whatever. With the worse cables, the signal would be so bad you would get no picture, or very bad signal degradation such that you'd get lots of errors shown by green sparkles on the monitor.
Out of the three cables I tried, it was the cable with the second shortest length that gives the best performance. I suspect it's some sort of slight impedance difference between the cables or something that causes the difference, but it goes to show that not all cables are the same!