I've worked as a dental hygienist for 6 years, and I have worked in the dental field for 10. I've seen all too often that a parent will decline xrays b/c of $, or "just don't want them", or "my kid doesn't have cavities" attitude. It is near impossible to detect cavities between the teeth w/o the xrays. If it can actually be seen clinically (w/naked eye), then usually that cavity is already pretty big. Our office practice is to take bitewing xrays once a year (beginning at around age 5, or when the child's mouth is big enough) and the panoramic (goes around your head for one big xray) every 3-5 years. We detect and fill cavities while they're small, before they grow into bigger problems. I've seen kids go from zero cavities to 5 or 6 within a span of a year, just b/c of their diet. Kids that drink a lot of juice, soda, cool-aid, and even milk are more prone to interproximal (between the teeth) decay. If your children have dietary habits like those, then yeah, I would definitely get the bitewings taken every year. You may be surprised at what they show, or they may show nothing. It may give you peace at mind knowing that you did what's necessary to help prevent decay problems. Then, you can bump up to 1 1/2 years between xrays if your kids have healthy teeth. I wouldn't go beyond that.
Some parents think that just b/c the decay is on a "baby" tooth, that it doesn't need to be fixed or addressed. Some of those "baby" teeth may be in the mouth until 12/13 years old. They can cause damage to the permenant teeth below or become abcessed and cause your child a lot of unnecessary pain/discomfort.
As far as the radiation goes, now a days its so minimal that the amount they're exposed to isn't any more than what you'd get by being outside all day.
Not all dentists are out there to make a quick $. Without dental xrays, it is difficult to do a "complete" dental exam. Some dentists frown on the declining of xrays as an inability to provide the patient the best care. So they're looking out for you, as a patient, and for themselves too, as a liability issue. If you decline xrays and then come in a few months later with a major problem, the responsibility lies with the patient, b/c it couldn't be diagnosed due to the lack of proper xrays. It legally can't be the dentists fault.
Hope this helps...and good luck