I learn langauges without a reason. 

Latin helps with modern Romance langauges. I don't know it well, but people who do (and who also know several Romance langauges) say it helps.
It satisfies your curiousity about their history.
Yes, there are books. If you mean modern books, some things are published in Latin, but it is mostly about Classical Philology etc. If you need a subject that is discussed exclusively in Latin, maybe it is some Vatican affairs:)
But there are also old books. If you're interested in science, then you may also become interested in its history and then you will want to read Latin texts.

Note though that Leibnitz mastered Latin with deciphering texts as a child rather than learning it in school.)))

It definitely worth doing especially if you are planning to learn a European language.I am studying Italian at the moment and knowing basic Latin really helps.