The number one mistake that many travelers make is forgetting to notify banks that they will be traveling. With all the things to do before leaving home, putting travel notifications on accounts often goes overlooked.
When your bank suddenly sees a charge pop up in Beijing on your debit card, the first assumption is that it has been compromised. Your card will be frozen, meaning you could find yourself overseas without access to funds and having to deal with making international calls to sort out the problem.
The situation is easy to avoid: set up a travel notification online or call the banks for your ATM and credit cards to let them know which countries that you'll be visiting soon.
You've just landed in a brand new country and now you need local currency. Exchanging money in the airport, while convenient, typically offers the worst deal. While those kiosks look safely official, they also must pay a hefty rent to be located in the airport. The currency exchanges in airports usually offer the worst rates. You're far better off using the ATM for local currency; even with the foreign transaction fees, you'll often end up with a better deal.
Tip: Know how to exchange money correctly and the current exchange rates for each place that you'll be visiting before you arrive.
It's entirely possible to have sufficient cash and still be "broke" in many developing countries. Those clean, crisp banknotes spat out by the ATM aren't always easy to break. The average shop or restaurant may have trouble breaking large bills; you may have to wait until change is found. Bus and taxi drivers most certainly won't have change, and some will be cheeky enough to ask for the difference, hoping that you'll relent out of desperation. Trying to pay a street-food vendor with a large-denomination bill is not only inconvenient for them, it's also considered bad form.
For starters, get creative with the amount of money you request from the ATM; choose an amount that will provide at least a few smaller bills. In Thailand, requesting 3,000 baht will yield three, 1000-baht bills that are hard to spend. Asking for 2,900 baht will provide you with a nice mix of smaller, easier-to-spend bills.
Along with creative ATM use, make a conscious effort to horde your small change as the locals do. It's all part of the game, just as negotiating for better prices and haggling in the local markets. If you're really stuck with large banknotes, you can often get change in bars on busy nights, chain restaurants and in your hotel.
Believe it or not, some countries want money both on your way in(visa fees) and out. You'll be asked to pay a departure tax in the airports as you are leaving. The process usually involves approaching a counter, paying the departure fee, then having your ticket stamped before proceeding through immigration.
While smart countries conveniently add the departure tax invisibly to the final cost of your airline ticket when booked, some still want you to pay in cash -- probably with local currency. If you don't save enough cash, you'll find yourself hitting the ATM at the airport one last time, paying transaction fees again and possibly leaving with local currency or trying to spend it on overpriced souvenirs before your flight departs. A few of the countries in Asia that require a departure fee to be paid in cash are Indonesia, Brunei and the Philippines.
If you choose to travel with your smartphone -- assuming that it is unlocked to work in foreign countries -- you could incidentally end up bleeding money if not careful. Many countries in Asia require that you purchase a SIM card and then add credit to it. Your phone's default settings are most likely set to take advantage of all the juicy, unlimited data on your network at home. In Asia, every time your phone performs a sync, updates an app or goes digging for the weather while not connected to Wi-Fi may be costing you credit which will have to be reloaded later.
Torn, marked up and faded banknotes are often pawned off to foreigners in the form of change. Depending on how much scrutiny is given, you may or may not be able to spend damaged paper currency later. You most certainly won't be able to exchange damaged banknotes on your way out. Follow the locals' lead and be firm about not accepting damaged currency that may be useful only as a souvenir later.