Dan Rutter's column in Atomic 62, Enough with the megapixels, already!, talked a lot about, oddly enough, megapixel counts on consumer-level digital cameras. While he did make a great point about megapixels no longer being much of a benchmark for camera performance - ie. more doesn't necessarily mean better - he only touched on the other critical part of any camera, digital or analog - the lens.
A camera is only as good as the lens it's attached to and, if you buy yourself a Single-Lens Reflex (SLR) camera you'll more than likely be able to remove and replace the camera's lens.
Why is this important? Why is your 3-megapixel Sony Cybershot not going to compete with a Nikon D70 or Canon 300D? True, the two latter cameras have superior image sensors and processors, but they can also support a variety of lenses. The fixed lens on the cheaper camera is exactly that -- cheap. Not only that, it's designed to cope with all sorts of situations, from landscape to portrait to macro. This presents a number of design challenges, some of which cannot be overcome.
Like the human eye, a lens is designed to focus light onto a sensor (for us, that would be the retina). And, just like your eye, a lens has to focus. If you have a bad lens then it's not going to focus that light properly onto the sensor and you'll end up with a fuzzy image, or one with bad colours. Lenses can cause a range of problems, from chromatic aberration (glowing purple edges on sharp colour or contrast transitions), vignetting (a darkening around the edges of the images), distortion (usually only found to a serious degree on large-range focal length lens like 18-125mm) and blurring. Obviously, a consumer-level camera with a fixed lens will be custom made for that camera, but it will be built to the same price ceiling as that camera and it will severely limit any creative impulses you may have.
Material quality also plays a role. If the lens glass isn't the greatest, it may diffuse the light before it hits the sensor. A bad lens can even enhance chromatic aberration and no matter how much you play with the lighting you'll still have problems. This is why people rave about lens from companies like Carl Zeiss, because they are damn nice.
Unfortunately, Carl Zeiss doesn't make lenses for Canon or Nikon cameras -- but you can buy special attachments to get Zeiss lenses for other cameras onto these more affordable models.
To give you an example of the power of interchangeable lenses, here's a shot I recently took with a fixed focal length 90mm Tamron macro lens. You can't do these kinds of shots with a kit lens, and there's no way you can do it with any fixed lens consumer-level camera.
If you're going to buy a camera, you might as well get one you can upgrade.