Traditional Tango Music
The music that is most frequently used for social tango today was recorded during the "Golden Age" of tango, approximately 1930-1950. It is a unique blend of classical instruments played with somewhat of a "street feel." The influences of tango music include percussive elements from African music, the traditions of Spanish guitar, Italian violin, classical piano, string bass, and a curious German instrument called the bandoneon. 
Here is a beautiful example of traditional tango music: Fumando Espero- Carlos di Sarli
We recommend this brief article by Clay Nelson to understand the relationship of the classical Tango music to the dance.
Neotango Music
During the past twenty years of the "tango renaissance," musicians and dancers have been experimenting with the introduction of electronic sound and world music to the social tango environment.
Listen to an example of neo-tango music:Tango Santa Maria- Gotan Project
 We recommend this article by Sharna Fabiano to learn more about contemporary trends in tango music.