I often shoot with flash, balancing it with continuous light. Because of the difference in nature of those two types of light (flash and continuous) you can get good control over the lighting situation.
In the above picture, the natural light can be seen in the shadows. The nice warm sunset-like light comes from a single Speedlite 430EX with an orange filter on it. By playing with the balance of continuous and flash I can exactly determine the darkness or depth of the shadows. By introducing some extra light, I was able to get this shot on a completely overcast day while it was slightly raining.
99% of the time I use flash it's off-camera, because I don't like the on-axis flash look. I know that even
David Hobby recently posted about on-axis fill, but I still don't really like the effect. By the way, if you don't know David Hobby, you should definitely check out his blog if you want to read up on lighting.
Many people write that baby photos cannot be taken with anything except natural light. I tend to differ. These photos of
baby Anaïs I shot with a combination of natural light and one or two flashes, simply in her parent's living room and the baby's room.
In the end I don't think it's about whether or not you want to use flash. I think it's all about the final picture you want to get, and what you can use to get that picture. If it's a drooling, nearly raining day, you can't make a picture like the top one with just a golden reflector, you'll have to introduce some extra light. The shot of Anaïs nibbling on her toe will probably have worked just fine with natural light and a large reflector. It's all about what you want, and how you can get it to work.