I really enjoy taking pictures of the kids. Over the years I've become better and my confidence has increased. And, because I seem to have the camera out all the time, the kids have gotten used to it; they are less likely to ham it up (though they do sometimes) and I get more natural pictures.
These suggestions, while by no means comprehensive, are a start to taking better photos of your kids. Once you get into it, you'll probably have more suggestions for me!
1. Really learn your camera
It's really easy to learn the basics of a camera: on and off, point and shoot, flash and no flash. But I'm talking about really learning your camera and trying new things with it. As technology has advanced, even low-end digital camera have a tremendous number of features. While you don't need to know every detail to take good photos, those features can complement your creativity and fun. Sit down with your user guide and learn about things like aperture, shutter speed, ISO sensitivity, and white balance. Most digital cameras offer automatic settings that do just fine, but taking the time to learn about manual settings and tweaks is well worth the time.
Also, there are companion books available for many DSLRs; they are well worth the investment.
2. Forget posing
Picture taking isn't just for events, it's for every day. If you only pull your camera out when everyone is dressed up and sitting still, you'll miss some great moments! Keep your camera handy for even the quietest, seemingly mundane moments. And forget about having your child say "Cheese!" - catch her in her everyday moments.
3. Look for the light
I've stopped using the Auto setting on my camera entirely. Too often, especially in in-between light, the flash goes off and then I have to deal with red-eye, less than ideal colors, and the situation is interrupted. Instead, I use the P setting and check white balance settings (I can do this quickly now), look for where the light is coming from, and adjust my point of view accordingly. Yeah, a few pictures have turned out a little dark or slightly fuzzy, but they were part of the learning process. The pictures I'm taking now feel more natural, and they are less intrusive when I am taking them.
4. Change your point of view
You don't always have to stand in front of your subject to take a photo. Get down on the floor and look up, or stand on a stool and look down. Especially with kids, getting down on their level often has great results. Likewise, your main subject doesn't always have to be in the center of your frame. Try offsetting your focal area up, down, or to the side.
5. Don't take just one photo
One of the most beautiful things about digital cameras is that you can take many, many pictures and delete ones you don't like. As such, don't be afraid to take lots of photos. You never know which one will be a good one, or you might end up with a really fun series of photos.
6. Get prints
Don't forget to print out your photos! Having a ton of pictures on your camera or computer is a fun thing, but there's still something special about putting pictures in albums and frames. Your framed prints can rotate, and kids love looking through albums to see their younger selves.
7. Practice, practice, practice
As with so many things, practice, practice, practice. The more you practice taking photos, the easier and more intuitive it will become, and the better photos you will produce!