Whether you're going on a quick weekend trip, or backpacking through Africa, you probably want to hold on to your valuables for as long as possible. With the right precautions, you are likely to be fine just about anywhere in the world.
I've visited 60 countries, including 6 months of backpacking in Africa, and only had one bad event. If I would have known these tricks back then, I would have avoided it.
#1: Don't show your riches
When you arrive in a new country, don't put all your cash in the same pocket, so that you have to pull out a big wad of bank notes every time you need to pay for something. Once you're in a safe environment, try to familiarise yourself with the different denominations, and keep most of your big notes separate from your pocket money.
Be discreet when using your smartphone in public. Apple products in particular seem to be magnetic to thieves. If you're in a high-risk country, maybe it's better to use your fancy laptop in your room of accommodation, instead of the lobby or common areas. I've put some ugly stickers on my MacBook, one of them covering the apple, to make it look less attractive and shiny.
#2: Stay alert in busy areas
This is absolutely key to avoid pickpockets, especially in touristic areas, and when entering and exit public transport. Confused tourists are prime targets for these types of crimes.
#3: Bring a padlock
If you're staying in hostels, you'll often find lockers that are possible to close with a padlock.
I also use it to lock my backpack if I'm checking it in at an airport, or putting it in the luggage compartment of a bus. When camping, I use it to lock the entrance of my tent, if I leave it behind while doing a hike. This is all about deterring petty thieves - while they still can steal the backpack itself, or cut themselves into your tent, they are more likely to go for easier targets.
If you have 179$ to invest in an extra bag, you might consider a Flak Sack. It's a good size for a day pack, and if you have a padlock and something sturdy to lock it on to, it's basically a portable safe.
#4: Get a concealed wallet
If you're doing a longer trip, it's worth investing in a concealed wallet. There are two main variants - the ones that hang around your neck, and the ones that attach to your belt.
I strongly favour the variant that attaches to the belt, as it can be flipped around to hang inside your pants. I put it directly in front of my crotch, and with normal jeans or loose fitting chinos it's basically invisible.
On this picture I'm carrying my passport, iPhone, credit cards, and some cash in an Eagle Creek Travel Pocket. That's basically everything I need to survive.
In the event of getting robbed, I think it's one of the last places the culprit would feel me up. I also have a pair of shorts that goes with a belt, and I use the wallet when sleeping in trains or buses to avoid someone stealing it while I sleep. If I feel suspicious about people in a hostel dorm, I also put it on.
The hang-around-the-neck variant is an easier target, and professional pickpockets will probably be able to cut it off your body without you ever noticing.
#5: Bring a backup card
I always bring two credit cards when I travel, and keep them in separate locations. One of them will normally be in my concealed wallet, while the other one will be somewhere deep in my backpack.
If I loose one of them, or my backpack or wallet gets stolen, I still have access to cash. One time, before I picked up this habit, my card suddenly malfunctioned on a trip to Istanbul. I had to spend countless hours to set up a money transfer through Western Union, and finding an agent that was able to help me. Don't depend on a single piece of plastic!
An added benefit is that every now and then an ATM will reject your card for no reason at all. Since I have my cards with different banks, occasionally one of them will go through when the other one fails. Hells yeah.
#6: Consider asking the reception to hold your valuables
Many hotels and hostels have some kind of system for storing valuables. As long as you trust the staff, this is probably safer than your room in most situations.
#7: Look like less of a target
If you're crossing Africa with public transport, or hitchhiking in South America, you'll probably be better off dressing down, than trying to look fancy.
Try to put on something modest and neutral the days you spend on the road. If you don't look like money, you're obviously less likely to get robbed.
When I travelled by public transport through Southern Africa, I stepped it up an extra notch. At night many cities turn dodgy, and occasionally I would have to cross through on foot to get to a bus- or a train station. To avoid attention, I would put on a hoodie and pull a Buff over my nose. I also carried my extra stuff in plastic bags. In the darkness, people would have to get very close to see that I was white (meaning foreigner), and no one as much as talked to me when I walked around.
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Final advice: be insured
No matter how many precautions you take, you well never be 100$ robbery proof. If you ever are confronted, and violence is a possible outcome, just give the robber what he wants, and you'll be out of the situation in no time at all. More often than not, the man on the other side is just as interested in a quick transaction as you are.
Before you set out, you should find an insurance company that caters to travellers, and read through their rules in detail. Everyone from Lonely Planet to the average travel blogger seem to recommend the same solution: World Nomads.
And yes: don't bring anything valuable that isn't covered, or that you can't live without.