i'm sure you've seen the bumper stickers... "my dad has more megapixels than your dad". they are mean-sprited and hurtful, and even though i am a proponent of free speech, i think they should be banned. although it has subsided a bit, there is much buzz to be had about megapixels. it's really nothing more than marketing hype. i would say that the casual picture taker is fine with anything more than 3 megapixels. you can very safely print an 8x10 with a 3 megapixel file. really, are you going to be putting those pictures of your dog on a highway billboard? most likely not, so there's no need for 15 megapixels. on the other hand, more megapixels does afford you the ability to crop your photos after with less loss of quality.
** warning - there is math in the following paragraph **
wait a minute, what is a megapixel anyway? well, a pixel is short for "picture element". it's basically a dot. a megapixel is 1,000,000 pixels. actually it's 1,048,576 pixels (2 to the 20th power), but who's counting? a really low resolution picture could be 800 pixels by 600 pixels. multiply those together and that gives you the number: 480,000 pixels, or roughly a half of a megapixel. let's keep with the standard aspect ratio of a typical photo which is 4:3 (800 over 600 gives a 4 to 3 aspect ratio). at 10 megapixels you have (10 (megapixels) * 1,048,576 (pixels in a megapixel) = 10,485,760 total pixels). think of it like a rectangle with a 4:3 aspect ratio and you get two equations:
(1) Area (in megapixels) = X * Y
(2) 4/3 = Y/X
take equation 1 and solve for X
(3) X = Area/Y
sub X into equation 2
(4) 4/3 = Y/(Area/Y)
solve equation 4 for Y
(5) Y = sqrt((4*Area)/3)
sub in megapixels into Area and solve for Y
(6) Y = sqrt((4*10,485,760)/3)
(7) Y = 3739 (rounded to nearest whole number)
sub Y into equation 3 to get X
(8) X = 10,485,760/3739
(9) X = 2804 (rounded to nearest whole number)
there you have it - a 10 megapixel shot will give you a photo with the dimensions of 2804 by 3739. now that i've written that out i realize it's pretty close to useless, but maybe it'll help you understand what all the numbers mean and where they come from.
before you start drooling over the pixel count on some new camera that you want, i must warn you that more is not always better. the sensor in the camera is only so big and the pixels can only be so small. in order to fit more pixels onto the sensor, they have to get squeezed way closer together to use every bit of sensor real estate available; the result is that the pixel density increases. i'll use an illustration to explain: imagine setting up bowling pins in a row evenly spaced 2 feet apart from one another. when you roll the ball toward the pins, chances are you're only going to hit one pin since the ball is not two feet in diameter. the ball is the photon of light and the pins are the pixels on the sensor. this would be a low-density setup. now get those pins so that they're all touching one another with no spacing between them. roll the ball again. you'll probably knock down three or four with the one ball. if you were using the amount of pins that fell down to determine how many balls were thrown, that would be a poor representation because it would be indicating three or four balls were thrown. this is roughly equivalent to the photons of light spilling over into adjacent pixels because they're too dense. on dslr cameras and probably even some point-and-shoots, the pixel density is specified. take a look at it when you're doing your comparisons - it's a much ignored but important camera specification.
next up: focal length