I am curious on whether any songs still exist from Roman Empire (before the split, so ca. 27 BC – 395 AD), from the Greek period (Alexander the Great to the end of the Seleucid Empire, so ca. 356 BC - 63 BC), or earlier.
What's the oldest known song that is still played today?
It depends what you mean by "still played today". The earliest known collection of notated music are the Hurrian Songs which contains the Hurrian Hymn No. 6 that was written circa 1400 BC. There is a recording of it here played on a Lyre.
In answering on whether it is "still played today", there is a Lyrist called Michael Levy who performs this piece and other ancient pieces of music. There is a video from 2012 of him playing this piece. That's the most recent recording I can find of it.
If you're not thinking of songs discovered by archeologers after centuries of being forgotten, but songs in active use from the time they were written, some candidates stand out:
"Dies irae" has been tracked back to the mid-late 1200's at the latest, with some possibility that it is even older still. Other Gregorian chants or religious songs can be equally old.
In the academic world, the song "Gaudeamus Igitur" has been known and sung since at least 1287. The currently used melody is only tracked back to the 1780's, but it is mentioned to be an old melody even in that source.
Some nursery rhymes are also very, very old. Many of the most well-known ones date back to the 1600's or earlier.
