I always carry at least some money in US and Canadian cash- crisp bills in large denominations (plus whatever useful foreign currency I might have had lying around from the last trip to the region).
Probably $500-$1500 in most cases. That, plus several ATM and credit cards (Plus System) and all three major types of CC's, kept in a couple locations and separate from the cash. I don't buy any foreign currency in advance nor do I generally sell the foreign currency upon leaving if I think I might be back in the next few years.
At the airport upon arrival, I usually get a couple hundred dollars worth of foreign currency (withdrawal from an ATM) to get started, and buy a coffee or something to get some change. That works in most of SE Asia, Europe, China, Japan etc. There are a few places where you won't find western ATMs, but there's usually a bank at the airport where you can change some money. If it's a situation where the ATMs won't work, more cash either from home or from the last country you visited where ATM cards are accepted. It's important not to carry too too much cash (many thousands of dollars equivalent total) or you could attract the attention of authorities trying to prevent money laundering. Although $10K is supposed to be okay in many places, I think they actually prick up their ears at far smaller amounts.
I keep a list of all ATM and credit card numbers and bank phone numbers, both in a munged written list and available in encrypted and munged form online (along with a scan of my passport, air tickets, visas, etc.), so I can easily call and cancel should there be a problem. Once I forgot a bank card in an ATM, called (using Skype, so it was almost free) and immediately cancelled the card.
In fact, worst case, should I happen to wake up naked in a ditch, the information online ought to be enough to get me back home eventually, with some inconvenience and tolerable monetary losses.
I do use a wallet (front pocket only) and have never had it stolen (though I did have some travelers checks stolen from the opposite pocket in a coordinated crush attack by pickpockets). Also a money belt, especially if I'm expecting to be alone in a risky area.
I also tend to trust hotel safes with at least some of my cash and most of my credit cards (perhaps unwisely). Most backpacks are really unsafe, especially many pockets that can be unzipped (often they find themselves unzipped behind you) but if you bury stuff down deep inside it's reasonably safe. I think I've been targeted by pickpockets and thieves about 10 times, and (so far) almost no losses.