Miles Davis - Kind of Blue
Charles Mingus - Ah Um
Those are both great suggestions. Other personal favourites of mine include...
Bill Evans Trio - Sunday at the Village Vanguard
John Coltrane - Impressions, Giant Steps, Blue Train (all great)
Art Pepper Meets the Rhythm Section
Sonny Rollins - Saxophone Colossus
Joe Pass - Virtuoso (solo guitar -- blows my mind)
Earlier Nat King Cole when he was still doing mostly jazz
The Quintet - Jazz at Massey Hall 1953 (Charlie Parker, Dizzy Gillespie, Bud Powell, Charles Mingus, and Max Roach.) If there is one album to define bebop, this is it.
Dave Holland Quintet - Not For Nothin'
Brad Mehldau Trio - Day is Done
Kurt Rosenwinkel - Deep Song
Wayne Shorter...Wayne's a hard guy to track, but it's all good. You can go with his stuff with the 1964-1968 Miles Davis Quintet (with Herbie Hancock, Ron Carter, and Tony Williams -- what a group!) or you can pick up anything by Weather Report (Heavy Weather is the popular choice here.) Or his more modern stuff -- it's a lot more freer, very cool stuff. I have albums from all three periods, and I love 'em all.
Herbie Hancock - Maiden Voyage. A jazz concept album? Crazy. Freddie Hubbard, George Coleman, Herbie, Ron Carter, and Tony Williams. GREAT record.
Chick Corea - Now He Sings, Now He Sobs. Recorded in 1968, Miroslav Vitous plays his ass off on this.
Oscar Peterson Trio - Night Train, We Get Requests. Also, the Live at the Blue Note series is amazing (OP, Ray Brown, Herb Ellis, and Bobby Durham guests on drums.) If you listen to these records (ESPECIALLY Night Train) you will have entered the Ray Brown School of Bass and Blues. Enjoy. He's a good teacher

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Thelonius Monk Quartet ft. John Coltrane - Live at Carnegie Hall. also, just about any Thelonius Monk recording is worth buying.