Ok, this is your resident non-dentist person.
the amount of radiation that is released when taking a small radiograph (x-ray) is a very small the tube they put up on your cheek directs the rays. they really don't "escape" out. howerver, for the peace of mind, either ask the dentist to skip the xrays if it's just a cleaning - no actual work/repair. OR have them use 1-2 lead aprons. I know plenty of dentists that continued to work while pregnant, including giving x-rays. they might have also worn a vest, but it's more cuz of the nature of the clinic we worked in, not so much of the specific space they were in.
Pan x-rays (the one that goes around your head) will give off more radiation, but it's on longer, etc. however, you should be fin with a lead apron.
2nd Trimester and early 3rd tirmester are the best times for dental work. That's when it poses the least amount of risk to a devloping baby. I have seen Drs turn away women with toothaches late in the 3rd trimester, only cuz they were 1-2 weeks away from due date and didn't want something to induce labor. (usually the patient's anxiety, nothing dental specific)
When you are getting specific work done - cavities, root canals, extractions, etc - xrays will be required. Otherwise, they just don't know what they are working with and you don't want them working in there "blind". That can pose a greater danger than the xray.
If you are high(er) risk in the pregnancy, talk to you OB first. But as Kelley said, Oral hygeine is very important - all the time, but esp during pregnancy.
Now, may I ask - why are people so afraid of the Dentist? I have never understood this fear.
ETA - please remember I am NOT a dentist. I worked in a clinic/school for 6 years. I picked up a lot of information in my time there (observing, talking to the doctors, etc). And my main focus was patients in pain and who hated the dentist.

But I am not a dentist. Just wanted to be clear!