If someone stole your stuff and then returned back to you and apologize should..

not really. i prefer let the perso go caused he already returned my stuff back with his own awareness and saying apologize to me. so what else? why i should keep dislike and revenge over him although i have those feeling too. it just be useless and only created many enemy in mylife. life is so short better to make new friends rather than new enemy ;)

It depends on what was stolen, and who it was. But most likely I would forgive them.

That depends on the people and the situations involved. For some, returning the property and apologising might be enough punishment due to humiliation. If they have stolen before, then something else may be needed. If it is a young person or a child, then I think some discipline is in order, for training purposes.