Greek is longer used than any other of the many Indo-European languages. This language has literally been in use for thousands of years and is still used today. For Westerners, it is a language used to transmit culture. It is used in religious writing and in diplomatic writing. It has long been associated with the educated classes of Western European culture, and is still used very heavily in universities today. It is spoken by 13 million people, both as a native tongue and as a second language. The language is most heavily-used in Greece and on the island of Cyprus.
Greek loses nothing to Latin in a contest of longevity and, unlike Latin, Greek is a living language. There is an ancient form of Greek, of course, that differs considerably from Modern Greek, but which is still spoken by some scholars. There are also numerous dialects of Greek. For many years, up until the 1970s, there was a common form of Greek and a more official form. The common form was cemented as the official form by law in the 1970s, eliminating the separation between those who spoke the language casually and the sometimes arcane language used in official business.
Greek is amazingly consistent over the ages. A Modern Greek reading a webpage could easily turn off their computer and read a text from a thousand years ago. Though the languages would be somewhat different, they would still be intelligible, one of Greek's truly unique features among languages.