The best advice I can give is that you thoroughly research the destination in guide books, on the Ministry of Foreign Affairs website and travel forums, so that you are aware of any passport-specific regulations before you go.
Many countries require travellers as well as citizens to carry photo identification on them at all times. It must at least be a national identity card, such as a Singapore IC. A driver's licence will not suffice.
Some countries, such as Thailand, Italy, Spain and Japan, do specify that travellers should carry their passports at all times, but interpretations of this law also vary.
In Italy, Spain and Thailand, a photocopy of your passport information page will usually be sufficient in the rare event that you are stopped by a policeman or immigration officer. If the authorities have additional questions, they will generally escort you back to your hotel to see the passport in person.
In Japan, the government advises travellers to carry their passports with them for inspection by an authorised officer because a foreigner's passport will describe the limits of their activities in Japan. Travellers are told to leave a photocopy of their passport in their hotel in case the original gets stolen or lost.
In China, you will need your passport if you are purchasing or picking up a train ticket at a train station. In South Africa, you will need your passport to change money.
In most countries you will need your passport if you are buying a SIM card. Unless you are travelling within the Schengen Area of Europe, it is essential to have your passport on hand if you are crossing a national border.
Unless a country's rules specify otherwise, I carry my passport with me only on days when it is absolutely necessary. Otherwise, I leave my passport in the hotel safe or locked in my suitcase, and carry a physical photocopy or a picture of my passport information page in my phone instead. In countries which require a visa, it is a good idea to photocopy or take a picture of the visa, and carry it with you as well.
Some people also keep scans of all their important travel documents - including flight itineraries, hotel reservations, important passport pages, a copy of their IC and visa information - on a USB drive or in their cloud which they can access easily from a hotel computer if their phone is stolen along with their wallet and passport.
On days when you need to carry your passport with you, keep it close to your body, tucked away in the inside pocket of your jacket, in a body pouch or deep inside a cross body bag, far away from the nimble fingers of pickpockets.
You are right to fear losing your passport or having it stolen while overseas. It is a travel nightmare, especially if you are travelling in a city or country without a Singapore Mission.
If your passport is stolen, the Immigration and Checkpoints Authority (ICA) says Singapore citizens should make a report to the local police immediately. Then proceed to or contact the nearest Singapore mission to apply for a Document of Identity so that you can return to Singapore, as it is not advisable to continue your travels without a passport.
You will need to bring along the police report, a passport photo, and verification of your citizenship (such as an IC, marriage licence or birth certificate). The Mission will verify your identity and furnish you with a temporary ID, which will cost about $15 and take up to two or three days or more, depending on where the Mission is located and how long it takes to verify your identity.
Upon returning to Singapore, you will need to go to the ICA Building in person to apply for a replacement passport. It will cost $80 to renew plus a $50 penalty for the loss or damage of a Singapore passport, which increases to an additional $100 if it has been lost or damaged more than once.
If the passport is found and returned to the holder after it has been declared lost, the traveller must surrender the recovered passport to ICA for cancellation within 14 days. Failure to surrender a recovered passport is a punishable offence and may result in a fine not exceeding $1,000 or imprisonment for a term not exceeding 6 months or both.
It is a hassle, to say the least.
At the end of the day, whether or not you carry your passport with you while touring is up to you, and very much dependent on your destination and your itinerary.
Unless a country specifies otherwise, it is better to be safe than sorry, and carry a copy of your passport rather than the real thing.
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