I took four years of Latin in high school, which equals probably 3 months of serious study. I recommend it as an intellectual diversion. I remember very little of it today, but it did open up my mind to grammar. Probably studying any other language would, but I liked that learning it wasn't an endorsement of any particular country.
I would say that the "opening your mind to grammar" is true of learning any new language. Obviously one like Latin where the grammar is very different than English might be more effective on that front, but with any new language you are forced to think about every word as a specific part of speech. It's like when someone tells you that your tongue doesn't fit in your mouth and you spend the rest of the day consciously thinking about something that is usually completely involuntary.
