It is a good idea to have your passport with you at all times in case you are stopped by the police and questioned. This is particularly true if you are travelling in border areas. Greek citizens are presumed always to have identification on them and the police presume foreign visitors do too. If you are arrested by police insist on an interpreter (diermi̱néas; say "the-lo dhi-ermi-nea") and/or a lawyer (diki̱góros; say "the-lo dhi-ki-go-ro").
Greek drug laws are the strictest in Europe. Greek courts make no distinction between possession and pushing. Possession of even a small amount of marijuana is likely to land you in jail.