This year's Nobel prize in Chemistry goes to Eric Betzig, Stefan Hell, and William Moerner for super-resolution fluorescence microscopy. This was on the list of possible prizes, and has been for several years now (see this comment, which got 2 out of the 3 winners, to my 2009 Nobel predictions post). And it's a worthy prize, since it provides a technique that (1) is useful across a wide variety of fields, from cell biology on through chemistry and into physics, and (2) does so by what many people would, at one time, would have said was impossible.
The impossible part is beating the diffraction limit. That was first worked out by Abbe in 1873, and it set what looked like a physically impassable limit to the resolution of optical microscopy. Half the wavelength of the light you're using is as far as you can go, and (unfortunately) that means that you can't optically resolve viruses, many structures inside the cell, and especially nothing as small as a protein molecule. (As an amateur astronomer, I can tell you that the same limits naturally apply to telescope optics, too: even under perfect conditions, there's a limit to how much you can resolve at a given wavelength, which is why even the Hubble telescope can't show you Neil Armstrong's footprint on the moon). In any optical system, you're doing very well if the diffraction limit is the last thing holding you back, but hold you back it will.

There are several ways to try to sneak around this problem, but the techniques that won this morning are particularly good ones. Stefan Hell worked out an ingenious method called stimulated emission depletion (STED) microscopy. If you have some sort of fluorescent label on a small region of a sample, you get it to glow, as usual, by shining a particular wavelength of light on it. The key for STED is that if another particular wavelength of light is used at the same time, you can cause the resulting fluorescence to shift. Physically, fluorescence results when electrons get excited by light, and then relax back to where they were by emitting a different (longer) wavelength. If you stimulate those electrons by catching them once they're already excited by the first light, they fall back into a higher vibrational state than they would otherwise, which means less of an energy gap, which means less energetic light is emitted - it's red-shifted compared to the usual fluorescence. Pour enough of that second stimulating light into the system after the first excitation, and you can totally wipe out the normal fluorescence.
And that's what STED does. It uses the narrowest possible dot of "normal" excitation in the middle, and surround that with a doughnut shape of the second suppressing light. Scanning this bulls-eye across the sample gives you better-than-diffraction-limit imaging for your fluorescent label. Hell's initial work took several years just to realize the first images, but the microscopists have jumped on the idea over the last fifteen years or so, and it's widely used, with many variations (multiple wavelength systems at the same time, high frames-per-second rigs for recording video, and so on). There's a STED image of a labeled neurofilament compared to the previous state of the art. You'd think that this would be an obvious and stunning breakthrough that would speak for itself, but Hell himself is glad to point out that his original paper was rejected by both Nature and Science.

You can, in principle, make the excitation spot as small as you wish (more on this in the Nobel Foundation's scientific background on the prize here). In practice, the intensity of the light needed as you push to higher and higher resolution tends to lead to photobleaching of the fluorescent tags and to damage in the sample itself, but getting around these limits is also an active field of research. As it stands, STED already provides excellent and extremely useful images of all sorts of samples - many of those impressive fluorescence microscopy shots of glowing cells are produced this way.
The other two winners of the prize worked on a different, but related technique: single-molecule microscopy. Back in 1989, Moerner's lab was the first to be able to spectroscopically distinguish single molecules outside the gas phase - pentacene, imbedded in crystals of another aromatic hydrocarbon (terphenyl), down around liquid helium temperatures. Over the next few years, a variety of other groups reported single-molecule studies in all sorts of media, which meant that something that would have been thought crazy or impossible when someone like me was in college was now popping up all over the literature.
But as the Nobel background material rightly states, there are some real difficulties with doing single-molecule spectroscopy and trying to get imaging resolution out of it. The data you get from a single fluorescent molecule is smeared out in a Gaussian (or pretty much Gaussian) blob, but you can (in theory) work back from that to where the single point must have been to give you that data. But to do that, the fluorescent molecules have to scattered apart further than that diffraction limit. Fine, you can do that - but that's too far apart to reconstruct a useful image (Shannon and Nyquist's sampling theorem in information theory sets that limit).
Betzig himself took a pretty unusual route to his discovery that gets around this problem. He'd been a pioneer in another high-resolution imaging technique, near-field microscopy, but that one was such an impractical beast to realize that it drove him out of the field for a while. (Plenty of work continues in that area, though, and perhaps it'll eventually spin out a Nobel of its own). As this C&E News article from 2006 mentions, he. . .took some time off:
After a several-year stint in Michigan working for his father's machine tool business, Betzig started getting itchy again a few years ago to make a mark in super-resolution microscopy. The trick, he says, was to find a way to get only those molecules of interest within a minuscule field of view to send out enough photons in such a way that would enable an observer to precisely locate the molecules. He also hoped to figure out how to watch those molecules behave and interact with other proteins. After all, says Betzig, "protein interactions are what make life."
Betzig, who at the time was a scientist without a research home, knew also that interactions with other researchers almost always are what it takes these days to make significant scientific or technological contributions. Yet he was a scientist-at-large spending lots of time on a lakefront property in Michigan, often in a bathing suit. Through a series of both deliberate and accidental interactions in the past two years with scientists at Columbia University, Florida State University, and the National Institutes of Health, Betzig was able to assemble a collaborative team and identify the technological pieces that he and Hess needed to realize what would become known as PALM.
He and Hess actually built the first instrument in Hess's living room, according to the article. The key was to have a relatively dense field of fluorescent molecules, but to only have a sparse array of them emitting at any one time. That way you can build up enough information for a detailed picture through multiple rounds of detection, and satisfy both limits at the same time. Even someone totally outside the field can realize that this was a really, really good plan. Betzig describes very accurately the feeling that a scientist gets when an idea like this hits: it seems so simple, and so obvious, that you're sure that everyone else in the field must have been hit by it at the same time, or will be in the next five minutes or so. In this case, he wasn't far off: several other groups were working on similar schemes while he and Hess were commandeering space in that living room. (Here's a video of Hess and Betzig talking about their collaboration).

Shown here is what the technique can accomplish - this is from the 2006 paper in Science that introduced it to the world. Panel A is a section of a lysozome, with a labeled lysozyme protein. You can say that yep, the enzyme is in the outer walls of that structure (and not so many years ago, that was a lot to be able to say right there). But panel B is the same image done through Betzig's technique, and holy cow. Take a look at that small box near the bottom of the panel - that's shown at higher magnification in panel D, and the classic diffraction limit isn't much smaller than that scale bar. As I said earlier, if you'd tried to sell people on an image like this back in the early 1990s, they'd probably have called you a fraud. It wasn't thought possible.
The Betzig technique is called PALM, and the others that came along at nearly the same time are STORM, fPALM, and PAINT. These are still being modified all over the place, and other techniques like total internal reflection fluorescence (TIRF) are providing high resolution as well. As was widely mentioned when green fluorescent protein was the subject of the 2008 Nobel, we are currently in a golden (and green, and red, and blue) age of cellular and molecular imaging. (Here's some of Betzig's recent work, for illustration). It's wildly useful, and today's prize was well deserved.