Finland’s national broadcaster YLI broadcasts the news in Latin (see here), so Latin is alive and well in Finland. It is still much used elsewhere, not least in the Vatican, and, indeed, Pope Benedict announced his resignation in Latin. Only a handful of Catholic priests speak Latin fluently. One of them is American Reginald Foster who runs a Latin summer school in Rome. He sounds quite a character – he gives his students 'home-play' (ludi domestici), not homework (see his Wikipedia page). Linguist Nicholas Ostler runs a few Latin sites on the internet (interretialis) (see here).
Latin was very important in the 16th and 17th centuries in Europe, but gradually fell out of use. The last major work in Latin to be produced in Britain was Isaac Newton’s Principia Mathematica of 1687, according to this interesting piece about Latin on the BBC website today.