Count Basie and his Orchestra in the 1938 recording of "Rockin' at the Woodside:
Thought of this because I was listening to a Basie tribute on KMHD on the way home last night that talked about how a lot of Basie's musicians didn't learn their parts from printed scores. Apparently Basie would lay down the theme and then the various sections would split up and riff on it until they'd got a track they liked, then the band would reassemble and jam.
As someone who never could play music without a printed sheet, I find that fucking amazing. These guys were some pretty incredible musicians, and that, along with the backbeat, is why I'll always love the hell out of jazz.