It's usually a good idea to take your money in a mixture of cash, credit or debit cards, and travellers' cheques. In an emergency, you can get people to wire you money. Before you set off, tell your bank and credit card company where you're going. You can set up payments to your credit card as well, so you don't arrive home to a massive bill. You can also make advance payments to your credit card, if you want.
Make sure you order your foreign currency a couple of weeks in advance, as places don't always have Estonian kroon or Vietnamese dong in. Some US dollars are always handy as well. Hide your cash in different places, like your money belt, a pocket, in your carry-on bag or even your sock. Carrying lots of cash is asking for trouble – and your insurance might not cover it if it gets stolen.
Most places have ATMs, but don't rely on them too much! It's a good idea to take both credit and debit cards (make sure your credit card has a PIN) as, if one doesn't work, you can use the other. Credit card fraud is quite high in some countries – be vigilant and check your statements carefully. Write down your credit and debit card numbers and keep them separate from the cards themselves. It's a good idea to take the phone number for lost and stolen cards too, so you can report any loss immediately.
Useful, as they can be quickly and easily replaced if they go walkabout. You don't always need them, but they are useful in countries with poor ATM facilities. As with your credit and debit cards, make a note of the numbers of your travellers' cheques, and keep them separate from the cheques themselves. Don't forget the phone number in case you lose them!
In an emergency, you can have money wired straight to you. It can be done online, by phone or in person at an office. You will have to collect the cash in person from an office, and will need to have some identification on you. It helps to have someone back home willing to do this for you, of course!