The Köln Concert by Keith Jarrett has to be one of my favorite jazz albums of all time, and it's also the best-selling solo jazz album in history. A friend in high school introduced me to it, telling me that he listened to it almost everyday and could sing along to most of it by heart. In 1975, Keith Jarrett recorded this concert at the Cologne Opera House in Germany, and it's just over an hour of pure improvisation. And while this sounds like it would be too free-form to repeatedly listen to, it has so much drive and structure that it's hard to believe that he made it up on the spot. In certain sections of the piece, he spends as much as 12 minutes improvising while vamping over a chord or chord pattern. It's so relaxing to listen to, but it still covers a wide range of emotional and musical ideas, from melancholy blues melodies to upbeat, ostinato rhythms.
Here's the first part of the first section of the piece: (it's traditionally divided into four sections, with the first being about 26 minutes long)
Here's another clip of Jarrett playing, this time from a different concert. Notice how physical he gets when he's playing: in certain parts of The Köln Concert, you can hear Jarrett banging on the piano and pedals to create percussion, and also sings along at other points.