It was usual for soldiers in the Republic to sing derisive songs during their general's triumph. Suetonius, in his Life of Caesar, records a couple of lines (§49):

All the Gauls did Caesar vanquish, Nicomedes vanquished him; [allusion to Caesar alleged pæderastic relation with the king of Bithynia]

Lo ! now Caesar rides in triumph, victor over all the Gauls,

Nicomedes does not triumph, who subdued the conqueror.

And also these ones (§51):

Men of Rome, keep close your consorts, here's a bald adulterer.

Gold in Gaul you spent in dalliance, which you borrowed here in Rome.

A specialist in Roman epigraphy could probably be more precise; some of the epigrams we frequently find engraved all over the Mediterranean world could probably be sung.

This thread:

http://www.reddit.com/r/AskHistorians/comments/1wq9ht/what_musical_instruments_were_there_in_0ce/

Starts our talking about Roman musical instruments, but then links to another thread which talks about Roman music (and modern reconstruction of Roman music) and Roman songs.

The responders seem to think that Roman folk songs (or Etruscan and Latin folksongs) were largely displaced by Greek music in Rome by the late Republican period.