Here's a far-from-definitive list of live jazz albums that rank at least among the artists' best work (in alphabetical order):

—Ran Blake, Vertigo
—Art Blakey, A Night at Birdland
—Dave Brubeck & Paul Desmond, Live at Oberlin, At Carnegie Hall, 1975: The Duets
—Jaki Byard, Live, The Last from Lennie's
—Betty Carter, The Audience
—John Coltrane, The Complete 1961 Village Vanguard Recordings, Live Trane, One Down, One Up
—Miles Davis, Live at the Plugged Nickel, Live in Stockholm 1960, Live at the Blackhawk, In Person at Carnegie Hall, Live Around the World, The Complete Miles Davis at Montreux
—Eric Dolphy, Live at the Five Spot
—Duke Ellington, Live at Newport 1956
—Bill Evans, Waltz for Debby, Sunday at the Village Vanguard, The Paris Concert, Last Waltz
—Dizzy Gillespie and Max Roach, Paris 1989
—Benny Goodman, Live at Carnegie Hall 1938
—Dexter Gordon, Homecoming
—Charlie Haden, The Montreal Tapes (especially with Paul Bley and Paul Motian), The Night and the City
—Dave Holland Big Band, Extended Play: Live at Birdland
—Shirley Horn, I Love You Paris
—Abdullah Ibrahim and Carlos Ward, Live at Sweet Basil
—Keith Jarrett, The Koln Concert, Tokyo '96, The Out of Towners, Radiance
—Lee Konitz, Live at the Half Spot, Thingin'
—Joe Lovano, Quartets
—Wynton Marsalis, Live at Blues Alley, Live at the House of Tribes
—Thelonious Monk and John Coltrane, At Carnegie Hall
—David Murray Big Band, Live at Sweet Basil
—Charlie Parker, Jazz at Massey Hall, New York City Town Hall June 22, 1945, The Complete Live Performances on Savoy, Boston 1952
—Bud Powell, Paris Sessions
—Sun Ra, Sunrise in Different Dimensions
—Sonny Rollins, A Night at the Village Vanguard, Our Man in Jazz, The Solo Album, G-Man
—Maria Schneider Jazz Orchestra, Days of Wine and Roses
—Mal Waldron, Explorations to the Nth Degree (with Max Roach), The Seagulls of Kristiansund
—John Zorn, Masada Live at Tonic, Masada Live in Jerusalem, Masada String Trio, Bar Kokhba Sextet
—Various artists, Happy 50^th Birthday Newport!