This isn't quite what you are looking for, but Euripides was very popular across the Greek world, both for the quality of his writing and for the melodies associated with it (in Greek plays, choral and other sections would be almost "sung"). How popular they were is demonstrated by Plutarch's description of he aftermath of the Sicilian Expedition, which was such a disastrous venture that virtually the entire Athenian force was either killed or captured. Those captured endured a rather terrible fate, being confined to the quarries outside Syracuse because the Syracusans, in a way, didn't have any real place to put them. But, the popularity of Euripides proved a savior to many of them. From Plutarch, "Nicias" 29:

Most of the Athenians perished in the quarries by diseases and ill diet, being allowed only one pint of barley every day, and one half pint of water. Many of them, however, were carried off by stealth, or, from the first, were supposed to be servants, and were sold as slaves. These latter were branded on their foreheads with the figure of a horse. There were, however, Athenians who, in addition to slavery, had to endure even this. But their discreet and orderly conduct was an advantage to them; they were either soon set free, or won the respect of their masters with whom they continued to live. Several were saved for the sake of Euripides, whose poetry, it appears, was in request among the Sicilians more than among any of the settlers out of Greece. And when any travellers arrived that could tell them some passage, or give them any specimen of his verses, they were delighted to be able to communicate them to one another. Many of the captives who got safe back to Athens are said, after they reached home, to have gone and made their acknowledgments to Euripides, relating how that some of them had been released from their slavery by teaching what they could remember of his poems, and others, when straggling after the fight, been relieved with meat and drink for repeating some of his lyrics. Nor need this be any wonder, for it is told that a ship of Caunus fleeing into one of their harbours for protection, pursued by pirates, was not received, but forced back, till one asked if they knew any of Euripides's verses, and on their saying they did, they were admitted, and their ship brought into harbour.

Granted, it is not unlikely that the story is a later invention or an exaggeration, but it does give a good indication of just how popular Euripides was.

A few weeks back I saw a documentary about the Happy Birthday Song, I wish I could provide a source but it was just a momentery blurb about the first recorded "hit", at least in our modern time. The wikipeida article talks about how it was wide spread in the early 1910s but wasn't credited to the author until the 1930s. Its origins actually go back even further, to the late 1800s in various forms.

From what I remember of the documentary, the Happy Birthday Song was written by a couple of school teachers, originally sang as "Good morning to you" to great the class every morning. Later the teachers put out a book about educating children, and they included this song as a way to break up the day. As the teaching aid became popular the song was adapted to celebrating birthdays, and Happy Birthday To You became the defacto song with which to extinguish candles.

That is a great question, and because it is hard to be sure what a "large" geographic, linguistic, or cultural barrier is, it is also very difficult to answer. That said, I think Lilli Marlene is a worthy addition to the thread. http://www.youtube.com/watch?v=8DXruigKRRc&feature=kp

Operettas pre-date what we call musical theater.

The ones you want to look at are Merry Widow by Franz Lehar written in German and played in many languages since. The signature waltz was very popular

Offenbach, Orpheus in the Underworld. You'll recognize the Can Can music

Sigmond Romberg wrote a number of early 20th century musical hits. His lyricist was occasionally Oscar Hammerstein. Try Stout Hearted Men or Softly as in a Morning Sunrise for cross cultural popularity

From a US standpoint Jerome Kern was probably the first to write a true American musical. Showboat is a good example.Old Man River is a song which was very popular.