Here is a playlist of the current show running on Live365. You can see a link to the show on the right. The playlist is in order. I identify the players on the show. If you want to check out the Monk tunes, go to the wonderful Jazz Discography Project.
Japanese Folk Song/Monk/Straight No Chaser/1966
Japanese Folk Song/Monk/Straight No Chaser/1966
Round Midnight/Monk/Misterioso/1958
Blue Monk/Monk/Thelonious Alone in San Francisco/1959Rhythm-A-Ning/Art Blakey and the Jazz Messengers with Thelonious Monk/1957
In Walked Bud/Monk/Underground/1967
Evidence/Monk/Live at the It Club/1964
Nutty/Thelonious Monk with John Coltrane at Carnegie Hall/1957
Ruby My Dear/Thelonious Monk with John Coltrane/1957
Epistrophy/Charlie Rouse/Epistrophy/
Friday the 13th/Thelonious Monk with Sonny Rollins/1953
Straight No Chaser/Mulligan Meets Monk/1957
Round Midnight/Charlie Haden/The Montreal Tapes/
Brilliant Corners/Paul Motian and the EBBB
Well You Needn't/John Stetch/Exponentially Monk/
Four in One/Anthony Braxton/Six Monk's Compositions/1989
Round Midnight/Steve Lacy and Mal Waldron/Live at the Dreher Paris 1981
Pannonica/Steve Lacy/5xMonk5xLacy/
Let's Cool One/Steve Lacy with Don Cherry/Evidence/
Bemsha Swing/Cecil Taylor/Jazz Advance/1956
Trinkle-Tinkle/Alexander Von Schlippenbach/Monk's Casino/2004
Boo Boo's Birthday/Alexander Von Schlippenbach/Monk's Casino/2004
Bright Mississippi/Alexander Von Schlippenbach/Monk's Casino/2004