I am not an EE or Physics expert but I HAVE been buying computers roughly every three to four years since 1981 (in '81 I bought my first, a Sinclair ZX81 and three years later a Commadore 64, toys really, and then my first IBM clone in 1987) , so I have 30 years of "field data" on this subject.
Even using my first IBM clone in '87 as the starting point (which had 640k of RAM and a 32MB hard drive), by multiplying everything by two every 18 months I get 10GB of RAM today and a 1TB hard drive. DAMN CLOSE!!!! Just a little too much RAM and a little less HD than what sits on my desk today.
Considering that this "law" was obviously intended as a general expectation of the exponential growth of computer power into the future, I was frankly shocked at how accurate it was over essentially three decades. If only "civilian space travel", "personal robots" and "hover cars" had seen similar exponential growth. Pity.
But from a STRICTLY user's perspective, Moore's Law seems to be holding fast FOR NOW.
moderator condenses multiple answers:
Although Moore's law explicitly deals with the number of transistors in a microchip, this is but ONE SINGLE benchmark in a much, much larger world of technologies advancing at an exponential rate.
To get hung-up on clock-speeds misses the point. One only need look at PassMark CPU benchmarks: http://www.cpubenchmark.net/high_end_cpus.html, to see that computers are getting VASTLY more powerful EVERY DAY.
The number of transistors on a chip is simply one component in enhancing today's computer power.
Though I am not Moore nor do I know him, I'm guessing that in a broader sense his law was an attempt to predict the exponential increase in computing power. He choose "number of transistors on a chip" as a CONCRETE and most important, QUANTIFIABLE yardstick as opposed to a much more "ambiguous and difficult to prove" assertion that "computer power will double every couple of years". To prove his theory, clearly something that could be easily measured was needed as the yardstick. But I will go out on a limb here and suggest he was predicting a larger trend dealing with EVERY aspect of computers.