You didn't mention exactly where you were travelling in these parts of the world -- major cities and resorts or into the countryside -- but having made a film in India, I've had plenty of experience in handling payments of all kinds.

With respect to that country: at major hotels, restaurants, etc. in the main cities any of the three major cards are accepted, as well as Diners. Visa and Mastercard can generally be used in smaller centres only at major outlets (i.e. chains of hotels, banks) but not at many smaller hotels, restaurants and shops. Cash is required for most transactions, and the 500 Rupee note the main denomination. You'll have bundles of them if you need to go into the smaller villages and towns for any length of time. Bank branches will cash traveller's cheques for a fee, and cash advances can usually be had on Visa and Mastercard. (Withdrawls from US/Cdn chequing or savings accounts don't seem to be possible and come out as cash advances keyed to you principal credit card.)

Hope this helps you.