While traveling I ran into two situations where my credit card was not accepted. I mainly use MasterCard. In China (although 10 years ago) Visa was accepted in most stores, but MasterCard was not. In the US, my MasterCard was rejected multiple times because it was a non-US CC number. This can be a real annoyance.
So could anyone recommend me a CC company which would give me global coverage? Or is this just not possible?
Generally speaking, from my experience VISA has wider coverage than MasterCard, but neither is 100%. So to get best coverage, it's recommendable having one of each.
Niche brands like American Express or Diners Club are not commonly accepted, so don't bother with them for international travel.
However, keep in mind, that in many countries, there are places where credit cards are not commonly accepted in shops. For example in the Netherlands you can pay anywhere with "PIN-card", which basically means only the debit card and only from local bank. It however seems to be slowly improving with introduction of EMVs (chip cards authorized with PIN).
As for Visa vs. Visa Electron or MasterCard vs. Maestro, I haven't seen any place which would accept the debit, electronic ones, but not credit cards. On the other hand there are places where only credit cards (not debit cards) are accepted (car rental, hotel reservation, etc).
Another issue is if your card supports EMV (known in the UK as Chip and Pin), which many US cards (and from some other countries) don't support.
You may have issues, especially in Europe, if your card doesn't support EMV (i.e. doesn't have a suitable smart chip on it). You're normally OK in hotels and very touristy shops, but outside there you may find your card refused, and not only for high value items, if it lacks a chip.
It's therefore recommended that you get a card with a chip on it (even if it's configured for Chip and Signature). See the wikipedia foreign cards section for more.
As far as I'm aware it's just not possible. Visa and Mastercard seem to always have the most coverage, Visa usually more often.
However, take Uzbekistan for example. Yesterday morning in Nukus, there were no ATMs. All banks but one only accepted Visa, and none took Cirrus or Plus cards. And only one bank took Mastercard.
Today in Khiva, there's only one ATM in town, and it's a Mastercard one!
I now hedge my bets and have more than one, plus some spare cash :)
Both Visa (Plus) and Mastercard (Maestro/Cirrus) have features on their websites where can you search a specific city anywhere in the world to find ATMs that will work with any Visa/Mastercard cards.
Presuming your ATM card is marked with either a Mastercard, Maestro or Cirrus logo then it should work at any of the ATMs listed on the Mastercard locator. Mastercard also have a Mobile App for iPhone, Android, and Blackberry.
If it's marked with either a Visa, Electron or Plus logos, then it should work at any ATM on the Visa locator, or on the mobile version.
As for Myanmar (aka Burma), they do indeed once again have ATM(s), but they are not part of any of the global networks, so they fit into your category 2. Given that the global networks are predominantly US based, I can't see this changing until trade restrictions are removed. The irony is that the US dollar is widely accepted - or at least it was when I was there 4 years ago.
Visa used to have three systems called Visa (for credit cards), Visa Debit (for debit cards), and Visa Electron (also for debit cards but only launched in select countries). When they launched their marketing campaign 'Go With Visa', they eventually simplified this so that most cards on their network these days - whether they are credit cards or debit cards - carry simply the Visa logo, and pass through the same payment processing network. Thus, as of now, a Visa card is one of the best bets you have. Still, there are caveats - a Canadian friend who came to Singapore found that he could only use his 'Visa Debit' logo card on select ATM networks that specifically supported it.
MasterCard has the main brand, and another one used only with debit cards called Maestro (again, only launched in select territories). Unlike Visa, an establishment or an ATM that can process MasterCard logo cards is not necessarily able to process Maestro (unless it supports Maestro too, of course).
In addition, many countries have their own payment networks that are massive in their own country but accepted nowhere else. China, for instance, has UnionPay which I think is the only domestic card allowed in China; it's also supported by quite a few Vietnamese, Malaysian, and Singaporean banks. Singapore too has its own system called NETS which until a few years ago was the only card you can use anywhere in the country, but that has changed now. Most of Asia has fairly good coverage for Visa and MasterCard now, with the former far more popular. At many merchant locations in Asia, you can only swipe a Visa card. Most bank ATM networks do support MasterCard, however.
For US-based travelers, I would highly recommend the Visa Signature. Most banks offer it with an annual fee, but, Capital One offers a no-fee option. They do not have any fee for foreign transactions, which otherwise would be 3%. It surely can add up if you have expensive taste ;) As far as acceptability is concerned, Visa, in my experience has the most options.
In East Africa (e.g. Kenya, Tanzania), Visa is much more commonly accepted than MasterCard. I had a Mastercard and only about half the ATMs & banks I went to accepted it, but just about all of them accepted Visa. I withdrew cash from the ATM (on my credit card) and used the cash locally, so I don't know how well accepted visa/mastercard are within shops, but I'd imagine cash is always much more often accepted.
