Having been on the receiving end of needles
twice, I would like to add that there are two types of needles with vastly different concerns if you get stuck:
HOLLOW: these are what people usually think of as needles: the things on the end of a syringe when you get your vaccinations. Since these have a lumen and thus can store infective material, they are much more dangerous IF contaminated. Needlesticks from these are usually from carelessness (dropped in the trash or left on a bed) or, ironically, from recapping the needle and missing the protective cap.
SOLID: these are the safety pins and suture needles which harbor far less infective material. When they stick someone they are additionally cleaned on the way in by the person's gloves, clothing, and skin; risk is further lessened, although not eliminated.