People can do what they want with their passport when in foreign countries but I've needed mine often enough to always carry it with me. Whether you do or not should be based on your own situation and where you are. Your passport should probably stay in your room safe if you are the type to get liquored up in an Eastern European sex club, are a scatter brain who is constantly losing things or lack the situational awareness to know when pickpockets are operating and don't know how to securely carry your passport.