The death of Moore's Law is often predicted, with arguments against a continued doubling covering topics from the speed of the electron (anyone recall claims that a 500mhz x86 chip wouldn't be possible?) to the thickness of silicon used in chip manufacture (once a layer is just 5 atoms thick, it will cease to act as an insulator, a problem that by the 'law' will need to be resolved in 20 years). But usually these are engineering issues, that a new approach invalidates. In a 2000 Nature article1 Seth Lloyd of MIT identified the extreme limits to computing as set by physics, not engineering.
As a way to grasp these distant limits, Seth considered the 'ultimate' laptop- that is, a computing device of 1kg within a 1 litre volume. This is in fact the "ultimate matter laptop" which clocks in at an impressive 1040 operations a second; a more potent still "ultimate laptop" that would permit 1051 operations a second is also identified.
Of course, we have no idea how to build such a device, but have a reasonable idea of what it would look like. Such a "laptop" would run at about a billion degrees centigrade, with near black hole density and requiring a 1026W power supply- that is, a medium sized star.
To help put such numbers into perspective, if the computational capacity of the universe itself is considered2, then it could have performed 10120 operations on 1090 bits since the beginning of time- in fact, an ultimate laptop would have existed then as a small part of the big bang. Humanity has managed an entirely respectable 1031 operations in its time- most of those in the last year (this is always true by exponential growth!). When does Moore's law require that we build an ultimate laptop? Just 200 years time.
So eventually Moore's law will lead us to a position where the universe is not enough (even if the optimal conversion of universe to ultimate laptops and power sources is achieved). However, the interesting thing about the ultimate laptop is not that we may one day build it, but that technology that currently works (albeit on a small scale) may render it unnecessary- by sidestepping the restraints of computing in a classical universe. That technology is quantum computing, and although still in its infancy (with 7 Qubit capacity the greatest achieived so far), the nature of quantum parallelisation is such that a 512 Qubit machine would spread it's work over 1.34*10154 parallel quantum universes- which is to say, far outstrip the sum total of classical operations the universe has managed so far. Even 256 Qubit permits 1.16*1077 calculations- more than our ultimate laptop offered per second.
Derived from a few notes on a lecture by Dr Jonathan Jones, University of Oxford, entitled "The Incredible Future of Computing"- part of the University of Bath Millenium Lectures series. (20/10/03)
1"Ultimate Physical Limits to Computation" Nature Vol 406 (31 August 2000)
2"Computational Capacity of the Universe" Physical Review Letters Volume 88, Number 23 (10 June 2002)