Latin is the ur-language that unites a lot of languages used in the west. If it’s true, as is claimed on Wikipedia, that the study of Interlingua helps one puzzle through Spanish better than the same amount of time spent actually studying Spanish, then Latin would be at least that useful, since Interlingua is basically Latin without inflectional endings.
It has also been mentioned that Latin helps with learning biological nomenclature. Of course, you can also just study the nomenclature by itself. Most do. Those, however, don’t end up learning much about Latin. The person who studies Latin, on the other hand, gets way out ahead in the study of scientific nomenclature and is in the enviable position of not merely memorizing, but understanding. Note that this advantage is cumulative with the advantage discussed above.
Latin is often cited as a good way to build up verbal scores in standardized tests, and not without evidence. But in fact, it simply stands to reason. 60% of English words come from Latin, and that jumps to 80% when you look at words of three or more syllables. How many syllables on average are you expecting per word in the SAT? Furthermore, those English words from Latin mean what they mean because of morphological rules that are not themselves carried over into English morphology, so English doesn’t teach you how to decode them. You can just study the English vocabulary directly, but the same amount of effort in Latin vocabulary plus derivational rules yields a rich English vocabulary as well. It’s also possible to just study the cheat sheet on Latin derivation, which will certainly help. But you won’t get any of the advantages mentioned in the previous two paragraphs, which are cumulative.
Latin is also a highly ordered and logical language, and is traditionally promoted as part of a complete curriculum that exercises rational faculties. Of course, you can and should study logic itself as well as mathematics and rhetoric. But it’s not as though the advantages of all these approaches to analytic training don’t stack. They are cumulative with those of Latin, which includes all the above discussed advantages as a free bonus.
It’s true that you don’t come out of a Latin class with the ability to communicate with living people (ignoring for the moment that the spoken Latin community is growing now that the internet is here to connect them). But let’s not pretend that high schools are cranking out fluent second language speakers either. You can parlay your halting high school French into continuing studies, but most people don’t. They let it wither and fade, and the advantage in principle that it’s an actual living language is rarely an advantage in fact. The opportunity cost for that advantage that never manifested is all the things above that Latin teaches you, which are cumulative.
Latin builds a diverse intellectual portfolio which pays reliable dividends however the market changes. Modern languages are high-yield investments with little liquidity.