As far as I've been able to find, I have not seen any long-term, controlled studies about the effects of ultrasound on fetal tissues. Women get it or they don't as they see fit, but there has never been a study where one group got it and a similar group didn't, and there is no established safe level of ultrasound. The American College of Obstetrics and Gynecology recommends AGAINST the routine use of ultrasound in pregnancy.
My personal feeling is thus: I will not be using a doppler to hear the baby's heartbeat before I go into labor (doppler is more constant sound waves while u/s imagery is intermittent). When I go into labor, doppler will only be used when the midwives in attendance want to get a heart rate and I don't feel like waiting for them to count. For ultrasound imagery, if there is a clinical indication to get one (fundal measurements are high or low, fetal movement has declined, blood work suggests a birth defect, etc) then I will get one after 20wks gestation. The tech will be admonished to get the information they need quickly and to limit unnecessary scanning. Students will not be allowed to practice on me.
Doppler and ultrasound are valuable tools, however they are used too frequently and unnecessarily during pregnancy to unknown benefit or detriment. Until there are more controlled studies following the effects of ultrasound on fetal tissue, I will not be an advocate for just getting one.