That really depends on what society you're talking about. It's normal for some natives of the south american rain forest to put holes through their lower lip and wear a large smooth wooden do well through the hole. That wouldn't be normal elsewhere. It's normal in america to eat beef but in parts of india it isn't. Normal is very subjective just as morality, evil and sin is. What is normal, moral, evil or sinful one place may not be somewhere else.
As far as American society:
Young women wearing exposing or revealing clothes.
Being offended by anything and everything.
Guys thinking they're a-holes; women thinking they're b-hes.
Having a smartphone or an android.