Piano Forum

To expand on what rachmaninoff_forever, Bach pieces in Jazz style are very common.

For example,  Siciliano, BWV 1031 -> Enrico Pieranunzi Trio - Sicilyan Dream

This thread talks about Art of Fugue Contrapunctus 2: https://music.stackexchange.com/questions/104257/jazz-bach-art-of-fugue-contrapunctus-2

Bach Preludes get a lot of play by Jazz musicians and have had a large amount of influence as well and so have the Goldberg variations and inventions. The C major prelude has acted similarly to a jazz standard would, with improvisation over the chord progression. Ave Marie is an example of that, because it has been interpreted by many different composers including Schubert who is a jazz like composer himself.

It should be noted as well that Baroque period pieces were played with a lot more liberty for ornamentations and improvisations not explicitly present on the sheet. Bach was also an adept improviser, and a good amount of his music is from improvisations or influenced/based in that structure.

Baroque music also heavily emphasized performance over everything else, which is how Jazz operates as well. Once you start getting into the Classical era is when you start have composers thinking of themselves more as composers than performers and getting particular about the way a piece is played. Rennasaince keyboard music also has had some impacts on jazz, specifically through the church modes and call/reponse elements.