It's impossible to say. It really depends on how you define adulthood, I guess.
Since the human body never stops changing and developing from the day you're born until the day you die, there's no single static stage we can pin down as "adulthood". It's a completely cultural and/or sociological construction.
If we choose to define adulthood as being able to reproduce with minimal risk to the body, I'd say it's 18 or so for women and 12-15 for men. However, everyone "develops" at different rates. (Males can reproduce with absolutely no direct physical problems, whereas females must be physically developed enough to carry the baby to term safely. This is why a far greater percentage of teenage pregnancies have serious complications)
Generally, it's safest to say "18 or so."
Further added to the complication, kids in the Western world are entering puberty earlier all the time. Some have attributed this to the increased amount of hormones in the food we eat - me, I don't know.