The modern Greek music reached its peak in the 50’s and the 60’s. Many famous performers, such as the Beatles, Edith Piaf and Milva, have interpreted some of the most popular Greek songs in their native language. Some other singers though, performed the songs in Greek.

1. Harry Bellafonte performed the song «Μες σ’ αυτή τη βάρκα» (Mes safti ti varka, Inside this boat) in Greek. http://www.youtube.com/watch?v=PHr_rm7Y-IY The song was composed by Manos Hadzidakis for the movie “Μανταλένα” (Madalena) in 1960 and was performed by Aliki Vougiouklaki, one of the most famous Greek actresses. http://www.youtube.com/watch?v=lCyhzsCFZMY
2. Sophia Lauren and Tonis Maroudas sang  together the song «Τι ειν’αυτό που το λένε αγάπη» (Tinafto pou to lene agape, What is this thing called love). It’s from the movie “Boy on a dolphin” (Greek title: Το παιδί και το δελφίνι, to paidi kai to delphini) by Jean Negulesco, filmed in Greece in 1957. Lyrics by Danai Stratigopoulou and Giannis Fermanoglou, music by Takis Morakis.
3. Georges Moustaki performed  the Greek song  «Κάπου υπάρχει η αγάπη μου» (kapou iparhei I agaph mou, My love must be out there somewhere).  Nana Mouschouri won the first prize at the Thessaloniki Song Festival in 1959 for her performance. The song was composed by Manos Hadzidakis.
4. «Μισιρλού» (Misirlou, Egyprian girl) is an old rebetiko song performed by many singers. The oldest registered version is probably by  Tetos Dimitriadis (1927).  Many famous musicians, made their own instrumental version of Misirlou. The best known is the version of Dick Dale that was used in the film Pulp Fiction, by Quentin Tarantino in 1994.
5. «Τα παιδιά του Πειραιά» (Ta paidia tou Pirea, Children of Piraeus) is one of the most popular Greek song worldwide. It was composed by Manos Hadzidakis for the movie “Never on Sunday” (Greek title: Ποτέ την Κυριακή, pote tin Kyriaki), directed by Jules Dassin. This song won an Oscar for Best Original Song in 1960. It was performed by Melina Merkouri.  In the late 90’s, Pink Martini have recorded their own version which is very popular in Greece

Source: http://www.musiccorner.gr/nees_kyklof/05/lounge.html