Maybe you know the song. Summertime In Wintertime. Great song by Badly Drawn Boy. In the Summertime, another classic.
But if it comes down to classicness in summertime, nothing compares to Gershwin's classic Summertime. This classical opera piece has become a jazz standard, and has been performed by numerous artists around the world. Of course, it has been performed as jazz, instrumental and with vocals; but also ska versions have been released, aswell as banjoëd versions. Steel drum groups have adopted the song. One of the best steel drum versions I heard is from Jack Warren: see Summertime.
And now, all of those performances of George Gershwin's classic have been collected under one special tag radio: summertime fm. You'll find famous interpretations by Miles Davis, Ella Fitzgerald(including a talkative live registration from 1958), Janis Joplin and of course Billie Holiday.