I have been asking friends, family and Facebookers for theirs. Join the discussion. It does not have to be a song with summer in the title. (I would include, for instance, both Bobby Darin's "Beyond the Sea" and the Showmen's "39-21-40.") But it should bring to mind the season in some way.
To get you started, some of the suggestions I have had already include Mungo Jerry, "In the Summertime": Ella Fitzgerald's version of "Too Darn Hot"; "Summer in the City" (where I would opt for Quincy Jones's version); LFO, "Summer Girls"; "Summertime" (Billy Stewart, Big Brother, and so on); Jamies, "Summertime Summertime"; Happenings, "See You in September"; Chicago, "Saturday in the Park"; Katrina and the Waves, "Walking on Sunshine"; Don Henley, "Boys of Summer"; just about everything the Beach Boys ever did; Bruce Springsteen's entire "The Wild, the Innocent & The E Street Shuffle"; War, "Summer," and more. Drop your suggestions in the comments section. And thanks!