Gosh, it so depends where.

For example, if you want to get see the fjords in western Norway, out among the fjords themselves, if you don't have Choice points (easy to earn tons of them during some promos, though not the current one) or Best Western points (slow to earn most of the time), you'll have to pay through the nose for indie hotels (not much competition). But even if you just want to cruises form back in Bergen, you won't find most of the "biggies" there. You'll find more Choice, you'll find SAS Radisson (is that part of Carlson or separate?), you'll find Scandic (which years ago was linked to Hilton HHonors but now is its own Scandinavia-specific chain), etc. I'm not sure which, if any, of the other "biggies" will do you any good even in Bergen.

But go to Madrid, and now there's no Choice. There's tons of Marriott, now that they've hooked up with AC Hotels. There's only one Hilton out at the airport. There's a couple Priority Club hotels in the city itself, but most are in random suburbs.

But go to Budapest, and Hilton has two great hotels, including the fabulous "Castle" (upon on a hill on the Buda side). And no Choice. Priority Club only has one IC in the city itself, and a Holiday Inn out in the suburbs (good if you are renting a car and doing side trips to the south and west of Hungary, no good if what you actually are visiting is Budapest proper on public transit).

But perhaps in Paris and London and Tokyo just about all the chains are there with several locations each.

Oh, then in South America: If you want to go Iguazu Falls, the only chain on the Brazilian side is a Best Western (but it's so inexpensive, you want to earn, not burn). On the Argentian side, insde the national park there's a fabulously-located Sheraton, but it's super expensive and also requires a lot of SPG points. In Patagonia, the only chain I've found is WyndhamRewards!

So there's no one or two or even three programs you can necessarily collect in and be sure they'll work everywhere in the world where hotels are expensive on cash and there's some chain hotel there you could get on points. (Obviously, if the hotels are cheap on cash, don't worry about points.)

Which is why you need to figure where overseas, and not just overseas, to figure out what program(s) you want to collect in.