The Guardian Travel supplement offers ten good (and varied) places to enjoy Live Music in Madrid. They include:
Cardamomo (Flamenco)
Café La Palma (Mix)
Populart (Jazz)
Las Tablas (Flamenco)
Honky Tonk (Rock)
El Junco Jazz Club (Jazz)
Las Carboneras (Flamenco)
Café Central (Jazz)
Clamores (Jazz, Flamenco, Pop, Folk and World music)
Sol y Sombra (Jazz, Soul, R&B and Flamenco)