Answer: there are many, mostly dead thousands and thousands of years ago. Thus: it all started with Homer and went on with people like Sophocles (theatre), Socrates, Plato and Aristotle (philosophy), many famous warriors and politicians of those times like Solon (law giver of Athens), others sadly famous like Alcibiades (Socrate’s pupil and famous betrayer of Athens) and many many others, among which many anonymous women (as usual), and other less anonymous, like Sappho, a poet from Mytilini.
After Alexander the Great, who conquered Asia Minor or Persia and whose origins are said Macedonian by some and Greek by others, a deep silent covered Greek territory for many historical years. Plotinos though was still Greek and thus most of the most famous theologians of those time. After there was an even deeper silence (Ottoman empire) and finally some awoke after 1830. Inside borders people like Macrogiannis are quite famous, but not very much liked outside for his obvious disliking of Occident. After, people like Callas, Onassis, and some other musicians I don’t like very much, got some notoriety abroad, as much as people as Melina Merkouri in cinema and the whereabouts. Two Greek poets got the Nobel price, among which Elitis, and some Greek novels inspired movies even in Hollywood (Christ’s last temptation is inspired of a Greek novel). A greek made up the cancer breast test for women, Papanikolau.
Lately Greek have become specially famous for their support of the 17th of November terroristic movement, support of Serbia during the Kosovo war and the hiding away of Ocalan, the PKK leader, in african countries. They managed though in the meantime to get some gold medals in the Olympics for weight lifting, a gold medal in 100 meters men in the Australian Olympics and the European Football Championship in Lisbonne 2004.
The most famous of all is though undoubtably Xristos Kakarantzas.