Alma La Doctora, a fellow music-lover, tipped me to another deservedly famous cantante last night: Eugenia León, so I looked her up on YouTube this morning, and here she is, in "La Paloma," (the dove) a song you'll probably recognize.
And something a little less traditional, "Los Pajaros Perdidos" (the lost birds) with a little taste of tango.
One last song, "Arrancame La Vida" which seems to translate to "start up my life." (Arrancar can also mean "boot up" when applied to computers: a little Spanish lesson bonus.)