Sometimes referred to as Neo-Latin. I'm going to list just a few examples.
For the most part, new volumes of Classical Latin and Greek texts from Oxfordand Teubnerare still appearing with prefaces in Latin. The few recent exceptions with prefaces and/or appendices in vernacular languages disturb me not a little.
Apart from Classical Studies, the only current communication in Latin of which I know is a Finnish website which still presents the news in Latin.
I own several volumes of volumes written by Catholic clergy in Latin in the 20th century, before the 2nd Vatican Council from 1962 to 1965, some consisting of theology, others of general news and notes from this or that order.
They say that the use of Latin persisted longer in the fields of mathematics and botany than elsewhere. For now I'm taking their word for it about botany. When it comes to math, as late as when Thomas Paine was blithely calling for ancient languages to be discarded, one of the leading mathematicians of the time, Leonhard Euler,was writing and publishing in Latin, as were, I presume, many of his contemporary mathematicians, and many more for quite a while after.
A little earlier, in the late 17th and early 18th centuries, Isaac Newton published his Philosophiæ naturalis principia mathematica in Latin; and Newton's rival -- or his punching-bag, depending upon how one views the matter -- Leibniz, although born and raised in Germany, was writing and publishing almost exclusively in Latin and French. As a young man Leibniz briefly met and corresponded with Spinoza, who wrote a few things in Dutch, but whose fame rests for the most part upon his Latin works, which today, for whatever reason, seem to be extraordinarily hard to find in untranslated book form. (Beaucoup translations of Spinoza's works. What th Heck are the translators translating from? as a character in William Gaddis' JR asked who was, it's not such a stretch to presume, representing Gaddis wondering in the face of the volume of fan mail he got about The Recognitions, are they all passing one copy around?)
Milton and Hobbes wrote quite a bit in Latin as well as in English. Milton's Latin poems -- and his Greek ones! Boy howdy! -- can be had in some anthologies;his Latin prose, although available translated everywhere you look, just like Spinoza's stuff, seem to be even rarer untranslated. (Or -- a possibility which my readers should assumed is implied. Always -- I'm just clueless.)
It would seem that a working knowledge of Latin was still assumed in some circles in the 17th century, not just in math and other sciences and philosophy, but among politicians and readers of history as well. In his collection of eywitness and near-contemporary accounts of the battle of White Mountain in 1620,Anton Gindely includes among his 44 sources 12 written in Latin. (Along with 20 in German, 3 in French, 4 in Spanish, 3 in Czech and 1 in English, which adds up to 43 and means, you're right, I counted wrong. But you get the idea.)
Some collections of letters give me the impression that Elizabeth I and Henry VIII of England wrote much more and much better in Latin, and possibly in French as well, than in English. (Which would mean that that scene in A Man For All Seasons where Henry meets Thomas More's daughter and the subject of Latin comes up, and she starts chattering away in the language and Henry can only haltingly respond with a few words, and he gets embarassed and angry, is historicaly waaaay off. Unless someone ghost-wrote all those letters of Henry's, but you know what? I doubt that!)
How far back into the past, into the history of western Europe, does one have to go to reach the point where Latin was more prevelant as a written language than the venacular? It really depends upon which group one considers, which profession or specialty, which social class, too. Latin seems always to have been more prevalent the higher one climbed on the social ladder. Perhaps the higher classes consciously used it as a means of separating themselves from the masses or of making the separation greater. Thomas Paine reacted by rejecting the language. I take just the opposite tack, I say it's just one more reason for us unwashed masses to learn it, one more way to seize what was denied our kind.