Every Wednesday evening at the B-Flat music lounge, the jazz shows are free. Conveniently located between Hackescher Markt and Rosenthaler Platz, the lounge is one of the city's best spots for jazz music. While they're open other nights of the week, the shows are only free on Wednesday.
The room fills up quickly so if you're looking for a table for the night, you'll have to show up early. People swoop in and out all night between the bands, though, so sometimes it's possible to snag a seat half-way through.