I see many emerging technologies that promise further great progress in computing. Here are some of them. I wish some industry people here could post some updates about their way to the market. They may not literally prolong the Moore's Law in regards to the number of transistors, but they promise great performance gains, which is what really matters.
3D chips. As materials science and manufacturing precision advances, we will soon have multi-layered (starting at a few layers that Samsung already has, but up to 1000s) or even fully 3D chips with efficient heat dissipation. This would put the components closer together and streamline the close-range interconnects. Also, this increases "computation per rack unit volume", simplifying some space-related aspects of scaling.
Memristors. HP is ready to produce the first memristor chips but delays that for business reasons (how sad is that!) Others are also preparing products. Memristor technology enables a new approach to computing, combining memory and computation in one place. They are also quite fast (competitive with the current RAM) and energy-efficient, which means easier cooling and possible 3D layout.
Photonics. Optical buses are finding their ways into computers, and network hardware manufacturers are looking for ways to perform some basic switching directly with light. Some day these two trends may converge to produce an optical computer chip that would be free from the limitations of electric resistance/heat, EM interference, and could thus operate at a higher clock speed. Would be more energy efficient, too.
Spintronics. Probably further in the future, but potentially very high-density and low-power technology actively developed by IBM, Hynix and a bunch of others. This one would push our computation density and power efficiency limits to another level, as it allows performing some computation using magnetic fields, without electrons actually moving in electrical current (excuse me for my layman understanding).
Quantum computing. This could qualitatively speed up whole classes of tasks, potentially bringing AI and simulation applications to new levels of performance. The only commercial offer so far is Dwave, and it's not a classical QC, but so many labs are working on that, the results are bound to come soon.
3D chips, memristors, photonics, spintronics, QC
I think Moore's Law is a steamroller. But, like the genomics sequencing technology highlighted in that post on Nuit Blanche, there are improvements just as fast, or faster than Moore's law. The improvements from better algorithms can yield exponential speed-ups too. Here's a graph (from this report) depicting the orders of magnitude improvement in linear solver performance: