Ear piercings and belly buttons are generally safe, but can become infected. Most other piercings(tongue, eyebrow)have risks of infection and added paralysis of nerves risks.
Piercings that just go through skin are safer. These are piercings such as ears. Ones that go through cartilage are a little more danerous. Ones that go though other body tissue, such as tounge or nipple, are the most dangerous.
Most piercings are safe as long as you get them done professionally. The safest though would be your ears, pretty much nothing can go wrong there. Your lip can cause some problems if done improperly but it's not common.
