Here we have one of the most durable tunes ever written. Originally written as a recurring aria for "Porgy and Bess," It has been re-harmonized in the some pretty radical ways and been taken in a wide variety of tempos. Yet, probably because of the strength of the melody, it retains its, well, Summertime-i-tude.
There is a widespread notion about Gershwin having been influenced by a Ukranian song. To quote WIkipedia: "The Ukrainian-Canadian composer and singer Alexis Kochan has suggested that he based the tune on a Ukrainian lullaby, Oi Khodyt Son Kolo Vikon (A Dream Passes By The Windows)."
I've had my research squad out searching for a copy of that song to see what resemblance it actually bears to Summertime, but so far, the samizdat has failed me.
In any case, herein are a few examples of the song. My criteria for choosing them was (1) how far away it ranges from the original and (2) how much I like it. Let's start off with a version of the original, performed by Harolyn Blackwell:
Billie Holiday had a popular success with her version:
Ella and Louis, of course:
Gil Evans arrangement with Miles Davis:
Janis Joplin live: