I am still studying Latin and enjoying it. But as far as benefits it is too early to tell. For now, I study it just the the enjoyment of it, but I would like to tell you the benefits that I have experienced from studying Classical Chinese, because I believe the benefits of Latin are probably similar. Classical Chinese is very different then how it is spoken. It tends to capture innate meanings and put them in a logical order, rather than be embedded in the arbitrary habitual patterns of speech. I believe that classical Latin was also very different then the way people spoke at that time. So the benefit to sum it up is:
It gives a person an acute awareness of the relationship between words and their ability to anchor down innate meaning. The ability to look at innate meaning a priori, before attaching words to it. And consequently, following it up with choosing the most precise words to express it.