At what age should I start getting mammograms?

40 years. If you have no factors which increase your risk for breast cancer then you should start getting yearly mammograms at age 40.
40 unless... According to the American Cancer Society, American College of Radiology, and others, annual screening mammography should begin at age 40. Screening may begin sooner if you are a BRCA carrier or are otherwise at high risk. If you have a lump or other symptom, see your doctor. Ultrasound, rather than mammography, would be the first imaging study of choice.
40 years. I follow the american cancer society recommendations, which is to begin yearly mammograms at age 40 and continue them yearly until age 75; after then, it is dependent on one's overall health. For women with a strong family history, i recommend beginning mammography 10 years earlier than when their relative was diagnosed, or age 40, whichever is earlier.