La Cumparsita is the song that is traditionally the last song played at a milonga. It signals to everyone that this is the last song, and that the milonga has concluded. There was a time when I was on a mission to collect as many versions of the song as I could find. At this point, I have forty  distinct versions.
It was written by Gerardo Hernán Matos Rodríguez, an amateur pianist and architecture student, in late 1915 or early 1916 by all accounts. He was 17 years old when he wrote it. It's important to note that he was a student in Montevideo - so the song originated in Uruguay.
The song has a very interesting story behind it - with changed lyrics, new music arrangements, ownership and royalties lawsuits (four or five), and plenty of drama over the years. It's often billed as "the most famous tango in the world". Astor Piazzolla called it "the most frighteningly poor thing in this world" in reference to the original score by Matos Rodríguez and its simple melody.
Here are a couple of links to good, in depth treatments of the song and its history:
Keith Elshaw's www.totango.net
Ricardo García Blaya's www.tototango.com
Note that both of these sites contain a wealth of information about tango music and all things tango.
Alberto Paz' www.planet-tango.com includes a lyrics translation of the re-written version. Alberto's site is well known for his lyrics translations, and also includes a wealth of information about tango.
This 1930 version, with the original lyrics sung by the opera singer Tito Schipa, is my personal favorite.