It's been my experience that in order to have a good time travelling in a foreign country, it's not actually necessary to speak the language. It's only necessary to try. Most people are flattered when they see that you, the exotic visitor from a distant land, find their country and customs so interesting that are trying to speak their language. Then, since they're happy, they'll go out of their way to make you happy.
Personally, I want to learn a lot of languages. First, I want to relearn Tamil and learn Sanskrit, so that a) I can speak to all my relatives in India, and b) understand what's going on during religious services. Next, I want to learn Spanish and Cantonese, because they are probably the two most common non-English languages I run into in the US. Japanese and French would be nice, for anime and art flicks, but not strictly necessary.
But sadly, it appears to be much harder to learn human languages than programming languages. :/