More pixels doesn't necessarily mean better quality: it just means that the image gathered by the lens and projected onto the sensor will be captured with more resolution. But if the optical quality is bad, and/or the sensor is tiny, the additional resolution would give you little advantage -if any at all. Far more important than the resolution, then, is the optical quality and the sensor size; for example, the Fujifilm F31fd (6 megapixels) will give you much better picture quality than, say, the Fujifilm Z20fd (10 megapixels), because the Fujifilm has better optics AND a larger sensor.
Of course, most manufacturers don't easily give information on their cameras' sensor size (you have to find that out in the specifications' page for the camera, either in the manufacturer's website or on specialized photography websites), and none give you an idea (at least not an unbiased one) of the camera's optical quality: you definitely have to look for professional reviews of the camera (DPReview, Imaging Resource, DCResource, etc).
But a generic, usually true thumb of rule is this: the smaller the camera (or its optics) and/or the longer its optical zoom, the less optical quality and smaller sensor you can expect it to have. The Casio EX-V7, for example, with its small body and its 7x, you can expect it to have (and indeed it has) poorer optical quality and a smaller sensor than, say, the larger, 6x zoom Canon PowerShot A650 IS.
As for pixels, it essentially amounts to the sensor size: if the sensor is larger, it can afford to have more megapixels without seriously compromising the image quality. Another pair of examples: the Fujifilm Z20fd, with its 10 megapixel, 1/2.5" sensor, won't have nearly as much quality as the Sony N2's 10 megapixel, larger 1/1.7" sensor.
Actually, most modern 12 megapixel cameras do have a somewhat larger sensor that can afford to have that many pixels, whereas most 7-8 megapixel cameras have a smaller sensor.
In short, choosing between long zooms, small cameras and good quality is a trade-off: you can't have all of it. Therefore, you have to decide what's more important to you: optical zoom, camera size or image quality.
As for memory cards, they rarely affect image quality in any way; they're just a convenience. The optimal camera would use SD and SDHC cards, because those have the best capacity/speed/price ratio, but sometimes you'll have to choose a camera that is the best in everything (for your own needs & preferences), except for the fact that they use the more inconvenient xD (Olympus/Fujifilm) or MemoryStick (Sony) card formats.