by Fazal Majid'sA digital photo is the output of a complex chain involving the lens, various filters and microlenses in front of the sensor, and the electronics and software that post-process the signals from the sensor to produce the image. The image quality is only as good as the weakest link in the chain. High quality lenses are expensive to manufacture, for instance, and often manufacturers skimp on them.
The problem with megapixels as a measure of camera performance is that not all pixels are born equal. No amount of pixels will compensate for a fuzzy lens, but even with a perfect lens, there are two factors that make the difference: noise and interpolation.
Noise
All electronic sensors introduce some measure of electronic noise, among others due to the random thermal motion of electrons. This shows itself as little colored flecks that give a grainy appearance to images (although the effect is quite different from film grain). The less noise, the better, obviously, and there are only so many ways to improve the signal to noise ratio:
Reduce noise by improving the process technology. Improvements in this area occur slowly, typically each process generation takes 12 to 18 months to appear.
Increase the signal by increasing the amount of light that strikes each sensor photosite. This can be done by using faster lenses or larger sensors with larger photosites. Or by only shooting photos in broad daylight where there are plenty of photons to go around.
Fast lenses are expensive to manufacture, specially fast zoom lenses (a Canon or Nikon 28-70mm f/2.8 zoom lens costs over $1000). Large sensors are more expensive to manufacture than small ones because you can fit fewer on a wafer of silicon, and as the likelihood of one being ruined by an errant grain of dust is higher, large sensors have lower yields. A sensor twice the die area might cost four times as much. A "full-frame" 36mm x 24mm sensor (the same size as 35mm film) stresses the limits of current technology (it has nearly 8 times the die size of the latest-generation "Prescott" Intel Pentium IV), which is why the full-frame Canon EOS 1Ds costs $8,000, and professional medium-format digital backs can easily reach $25,000 and higher.
This page illustrates the difference in size of the sensors on various consumer digital cameras compared to those on some high-end digital SLRs. Most compact digital cameras have tiny 1/1.8" or 2/3" sensors at best (these numbers are a legacy of TV camera tube ratings and do not have a relationship with sensor dimensions, see this article for an explanation).
For any given generation of cameras, the conclusion is clear - bigger pixels are better, they yield sharper, smoother images with more latitude for creative manipulation of depth of field. This is not true across generations, however, Canon's EOS-10D has twice as many pixels as the two generations older EOS-D30 for a sensor of the same size, but it still manages to have lower noise thanks to improvements in Canon's CMOS process.
The problem is, as most consumers are fixated on megapixels, many camera manufacturers are deliberately cramming too many pixels in too little silicon real estate just to have megapixel ratings that look good on paper. Sony has introduced a 8 megapixel camera, the DSC-F828, that has a tiny 2/3" sensor. The resulting photosites are 1/8 the size of those on the similarly priced 6 megapixel Canon Digital Rebel (EOS-D300), and 1/10 the size of those on the more expensive 8 megapixel DSLR Canon EOS-1D Mark II.
Predictably, the noise levels of the 828 are abysmal in anything but bright sunlight, just as a "150 Watts" ghetto blaster is incapable of reproducing the fine nuances of classical music. The lens also has its issues, for more details see the review. The Digital Rebel will yield far superior images in most circumstances, but naive purchasers could easily be swayed by the 2 extra megapixels into buying the inferior yet overpriced Sony product. Unfortunately, there is a Gresham's law at work and manufacturers are racing to the bottom: Nikon and Canon have also introduced 8 megapixel cameras with tiny sensors pushed too far. You will notice that for some reason camera makers seldom show sample images taken in low available light (like these ones taken at ISO 800 with my Canon 10D)...
Interpolation
Interpolation (along with its cousin, "digital zoom") is the other way unscrupulous marketers lie about their cameras' real performance. Fuji is the most egregious example with its "SuperCCD" sensor, that is arranged in diagonal lines of octagons rather than horizontal rows of rectangles. Fuji apparently feel this somehow gives them the right to double the pixel rating (i.e. a sensor with 6 million individual photosites is marketed as yielding 12 megapixel images). You can't get something for nothing, this is done by guessing the values for the missing pixels using a mathematical technique named interpolation. This makes the the image look larger, but does not add any real detail. You are just wasting disk space storing redundant information. My first digital camera was from Fuji, but I refuse to have anything to do with their current line due to shenanigans like these.
Most cameras use so-called Bayer interpolation, where each sensor pixel has a red, green or blue filter in front of it (the exact proportions are actually 25%, 50% and 25% as the human eye is more sensitive to green). An interpolation algorithm reconstructs the three color values from adjoining pixels, thus invariably leading to a loss of sharpness and sometimes to color artifacts like moiré patterns. Thus, a "6 megapixel sensor" has in reality only 1.5-2 million true color pixels.
A company called Foveon makes a distinctive sensor that has three photosites stacked vertically in the same location, yielding more accurate colors and sharper images. Foveon originally took the high road and called their sensor with 3x3 million photosites a 3MP sensor, but unfortunately they were forced to align themselves with the misleading megapixel ratings used by Bayer sensors.
Zooms
A final factor to consider is the zoom range on the camera. Many midrange cameras come with a 10x zoom, which seems mighty attractive in terms of versatility, until you pause to consider the compromises inherent in a superzoom design. The wider the zoom range, the more aberrations and distortion there will be that degrade image quality, such as chromatic aberration (a.k.a. purple fringing), barrel or pincushion distortion, and generally lower resolution and sharpness, specially in the corners of the frame.
In addition, most superzooms have smaller apertures (two exceptions being the remarkable constant f/2.8 aperture 12x Leica zoom on the Panasonic DMC-FZ10 and the 28-200mm equivalent f/2.0-f/2.8 Carl Zeiss zoom on the Sony DSC-F828), which means less light hitting the sensor, and a lower signal to noise ratio.
A reader was asking me about the Canon G2 and the Minolta A1. The G2 is 2 years older than the A1, and has 4 million 9 square micron pixels, as opposed to 5 million 11 square micron sensors, and should thus yield lower image quality, but the G2's 3x zoom lens is fully one stop faster than the A1's 7x zoom (i.e. it lets twice as much light in), and that more than compensates for the smaller pixels and older sensor generation.
Recommendations
If there is a lesson in all this, it's that unscrupulous marketers will always find a way to twist any simple metric of performance in misleading and sometimes even counterproductive ways.
My recommendation? As of this writing, get either:
An inexpensive (under $400, everything is relative) small sensor camera rated at 2 or 3 megapixels (any more will just increase noise levels to yield extra resolution that cannot in any case be exploited by the cheap lenses usually found on such cameras). Preferably, get one with a 2/3" sensor (although it is becoming harder to find 3 megapixel cameras nowadays, most will be leftover stock using an older, noisier sensor manufacturing process).
Or save up for the $1000 or so that entry-level large-sensor DSLRs like the Canon EOS-300D or Nikon D70 will cost. The DSLRs will yield much better pictures including low-light situations at ISO 800.
Film is your only option today for decent low-light performance in a compact camera. Fuji Neopan 1600 in an Olympus Stylus Epic or a Contax T3 will allow you to take shots in available light without a flash, and spare you the "red-eyed deer caught in headlights" look most on-camera flashes yield.
Conclusion
Hopefully, as the technology matures, large sensors will migrate into the midrange and make it worthwhile. I for one would love to see a digital Contax T3 with a fast prime lens and a low-noise APS-size sensor. Until then, there is no point in getting anything in between - midrange digicams do not offer better image quality than the cheaper models, while at the same time being significantly costlier, bulkier and more complex to use. In fact, the megapixel rat race and the wide-ranging but slow zoom lenses that find their way on these cameras actually degrade their image quality over their cheaper brethren. Sometimes, more is less.
Updates
2005-09-08: It seems Sony has finally seen the light and is including a large sensor in the DSC-R1, the successor to the DSC-F828. Hopefully, this is the beginning of a trend.
2006-07-25: large-sensor pocket digicams haven't arrived yet, but if you want a compact camera that can take acceptable photos in relatively low-light situations, there is currently only one game in town, the Fuji F30, which actually has decent performance up to ISO 800. That is in large part because Fuji uses a 1/1.7" sensor, instead of the nasty 1/2.5" sensors that are now the rule.
in 1888. 
