Since I sing and play (guitar) for a lot of retirement residences and senior centers, there's a lot of demand for the popular & jazz standards from the '20s, '30s, '40s, etc.  I don't mind at all, since there are so many great songs to choose from.

I love Louis Armstrong, Cab Calloway, Duke Ellington, Ella Fitzgerald, Billie Holiday, Ruth Brown, 
Louis Prima, The Inkspots, and a slew of other jazz musicians from "The Jazz Era, not to mention Brubeck, Miles Davis, Pete Fountain, Les Paul, etc.   Re composers, I love Gershwin, Hoagy Carmichael, Harold Arlen, etc.  My favorite pieces to perform include the following, which I would put in the broad category of jazz:
Up A Lazy River
Someone To Watch Over Me
Come Sunday (Duke Ellington)
Minnie The Moocher
Stardust
Dream A Little Dream of Me
Lazy Bones
Undecided
Java Jive
Nevertheless
That Old Black Magic (a la Louis Prima and Keely Smith)
As Time Goes By
Ain't Misbehavin'
Misty
Sing, Sing, Sing
Deep Purple
Twilight Time
Any Time/All of Me (medley)
Moondance (I'd call it a jazz piece)
Stormy Weather
Blues In The Night
Is You Is Or Is You Ain't My Baby?
Shoo-fly Pie and Apple-Pan Dowdy

I've had to broaden my guitar skills (especially expanding my arsenal of chords) as I started branching out from folk and country/western.  I think one reason I like doing jazz standards is that my voice is suited to that kind of music as well as or better than to traditional folk  (though I didn't think so when I first started out).

Glad to hear there are other "folkies" who appreciate jazz in its various forms, too.

Genie