Robert Scoble does some math comparing digital to film photography. He describes a number of advantages that digital photography has over film, but he misses one the most important ones: You take better pictures with digital ... because you take more of them.
There's no marginal cost to taking additional photos with a digital camera so shoot away. When I am taking photos of the kids (or anything else for that matter) I usually shoot 5-10 of virtually the same thing. Not to take away from all of the skills possessed by professional photographers, but I believe this is the first key to their ability to take great pics. With people shots it allows you to capture a selection of facial expressions, one or two of which may actually be good ones. With all shots it allows you to adjust composition, exposure, flash, etc.
One thing this aspect of digital photography has done is made me want a better camera. I have a 2 megapixel Olympus C-2020Z. It's a great camera that we've had for 2.5 years and with which we've taken 4,668 pictures so far (actually, those are how many we've kept; we've also deleted thousands; that's the point). While more pixels would be nice what I'm really after is a faster camera. I miss a lot of shots of the kids in motion because the camera is going through all sorts of machinations between shots. Make this a key criteria when buying a digital camera. I think I read that there's no agreed upon standard for measuring and reporting shutter lag time (I think that's what this is referred to), so you'll have to play around some. As a slide aside, this is an oft-overlooked (or at least underplayed) aspect of digital camera reviews.
Finally, I disagree strongly with comments that equate 2 megapixel pics with a maximum acceptable output of 5x7". I regularly get prints from Ofoto at 8x10" and to my reasonably discerning eye they are every bit as good as shots from my old Pentax SLR.