Thank God that I never lost my passport while I was traveling the world! During my trip I did meet travelers that did have their passports stolen while abroad. Trying to get another passport is a headache that you don't want or need during your world trip. There are a couple of things that you do not want to lose while you are traveling: atm card, credit card, and most important your passport.
Before I left on my trip I had made two color copies of my passport and had them lamented. I hardly ever carried my passport with me while I was walking around cities being a tourist or while I was going out at night. I would keep my passport back where I was staying. Most hostels have a lock box for you to keep your belongings in. Some hostels have lock boxes but no locks. So on your trip I would also suggest that you bring your own pad lock to lock up your things and keep them secure.
I did keep a copy of my passport in my pocket just in case I needed some sort of identification for whatever reason. During my trip I was doing volunteer work in Manta, Ecuador. Manta is located on the beach, and I had a day off so I was headed to the beach. On a Saturday afternoon I was crossing the main steet which is one block from the beach. As I was crossing the street a police car went by, stopped, and reversed back to me. The cop waived me over and started speaking to me in spanish. Thank God that I can communicate a little bit in Spanish...he was asking me what I was doing in Manta, and saying that he is part of the immigration department (which he was clearly not). He asked me for a copy of my passport. I didn't have my passport, but I gave him a copy of the passport. He asked me for the real one, but I told him it was back at the guest house. He was satisfied with that and then let me on my way.
I never once got ID to go out at night outside of the States. So don't worry about having your ID to show your age while traveling abroad unless you are under 18.
I don't know what would have happened if I didn't have a copy of my passport. Maybe nothing? But I know that at least by carrying a copy of my passport instead of the real one I avoided losing the real one and I had ID on me incase somebody asked. If you passport is stolen or lost over seas visit the State Department's website.
