Accepting cards from most locations isn't actually difficult any longer with Stripe, Braintree, Paymill, and others. US cards aren't special in terms of being able to accept them; they're just regular Visa/MC/Amex/Discover/whatever cards.
The neglected payment methods are the country specific ones. Some major countries have very low credit-card penetration, for example in the Netherlands. The common internet payment method there is iDEAL which is a kind of two factor authenticated bank transfer. Even debit cards in the Netherlands have two distinguishing features: there isn't a PAN number on the card which makes it impossible[0] to use online in the way you'd use an embossed Visa/MasterCard, and the Dutch banks all issue their debit cards under the Maestro and V-Pay schemes.
[0] Not really, but very few people know what their debit card's PAN number is. It's possible to calculate the hidden PAN number as it's usually just a regular Maestro card, or to just scan it off the card using NFC and an appropriate app.
The neglected payment methods are the country specific ones. Some major countries have very low credit-card penetration, for example in the Netherlands. The common internet payment method there is iDEAL which is a kind of two factor authenticated bank transfer. Even debit cards in the Netherlands have two distinguishing features: there isn't a PAN number on the card which makes it impossible[0] to use online in the way you'd use an embossed Visa/MasterCard, and the Dutch banks all issue their debit cards under the Maestro and V-Pay schemes.
[0] Not really, but very few people know what their debit card's PAN number is. It's possible to calculate the hidden PAN number as it's usually just a regular Maestro card, or to just scan it off the card using NFC and an appropriate app.