La Cumparsita
La Cumparsita is the most famous of all tangos and has been recorded by almost every tango orchestra. Its fame has developed over the years as it is often played as the last song of the evening at milongas. Sometimes you even hear two different versions of La Cumparsita played at the same milonga.
Uruguayan Tango
Ironically, the most famous Argentine tango tune was originally written by a Uruguayan, Gerardo Hernán "Becho" Matos Rodríguez. If you research tango history you find that there is significant input from Uruguay and Montevideo across the estuary of the Río de la Plata (River Plate) from Buenos Aires. Originally written as a march, it was shown to tango orchestra leader Roberto Firpo, when he was playing in Montevideo, as people thought it could be a tango.
Firpo rearranged the tune and added some bits from a couple of his older tunes and recorded it in 1916, a recording that still exists. However, it was released as a B-side and, although it enjoyed some success for a few years, it started to fade in popularity.
New Lyrics & Controversy
In 1924 the current lyrics to the song were written by Argentine Pascual Contursi, who recorded the song with a new title "Si Supieras" ("If you knew"). In this format it became a big hit and was being played by all the tango orchestras. The original composer Gerardo Matos Rodríguez was living in Paris and heard Si Supieras being played by Francisco Canaro, a famous tango orchestra leader and fellow Uruguayan. (If you know about his life, you'll realise that "If you knew" would make a great title for his biopic. Ed.)
What followed were years of legal arguments over the title and royalties, with the original title La Cumparsita being reinstated; Orquesta Típica Victor having recorded a version titled La Cumparsita in 1926. It did take a few years longer for the distribution of royalties to be finalised.
This tango is so famous that it has its own Wikipedia page