If you launch a product to a few different countries, does it make sense to do usability testing in all those different countries?

Perhaps. You have to consider how your product is used and how the users will sensorially interact with it. If you have a website, for example, you could probably assume similar US and UK usability -- but now consider layout for Semitic languages which are read right-to-left -- or consider ideographic languages where the ideographs could interact with other graphical elements in a way wholly irrelevant with the languages you're familiar with.

If you have a physical product, the question is conceptually the same, but the actions are different. You have to consider how users in a given culture use and interact with products of that sort. Different cultural memes, ways of learning and expectations can effect usability.

There are some simple ways to do these things if you have a small budget. You could easily go to craigslist and recruit 10-15 natives of a given country or region. Give them the product or have them use the website (for 60-90 minutes), video it (with their permission of course and for reasonable compensation), and you'll get a potentially useful indicator of usability. If you're P&G or Microsoft, you've got the budget to test against statistically valid sample sizes pretty much everywhere in the world. You don't have that, so you need to use some heuristics.

Good luck to you. Should you have any questions, I'd be happy to discuss.

The quick answer is yes, it always makes sense to do usability testing where there are variations in cultural preconceptions, market maturity, language proficiency (you don't mention if it will be available in many different languages) and the like.

Whether or not you do usability testing in all countries of course also comes down to what resources you have and how you intend to make use of the findings. Many times I find it appropriate to launch and test iteratively along the way, making sure you have the budget to make continuous small improvements, making sure to have feedback mechanisms in place and placing more effort in testing and managing areas which clearly are more critical for the end-user satisfaction. But you'd never want to launch before you have something that you yourself are satsified with. My recommendation would be to do quick online tests to make sure you are not entirely off-base, and then make sure to set the iterative launch-measure-analyze-prioritize-fix process in motion.

It can be safely assumed that people from different cultures will behave differently with the same product. They have different aspirations, motivations, circumstances in which they use a product, use cases, and social meanings.

If you are launching the product in countries that are very different culturally, it makes sense to conduct usability testing in different countries.