Below is a list of tunes I frequently use with beginners. It is in no way intended to be an exhaustive list! Lead sheets for all of these tunes are readily available. Check the "Materials" page for my most used resources, and for some of my supplemental materials that you may find useful.
I've organized it into three sections; section one includes tunes I start with for the youngest musicians and most novice improvisers. These are tunes my older students revisit frequently, though, too. One of the special things about improvising is that there's no true equivalent of "Hot Cross Buns" from your beginning band book -- your students and you can keep returning to the first lead sheet you ever played and find new things to say (unless you do "Hot Cross Buns" improv with your beginning band, which I would highly recommend!).
I.
Bags' Groove by Milt Jackson
Blues by Five by Red Garland
Blues in the Closet by Oscar Pettiford
Cantaloupe Island by Herbie Hancock
Impressions by John Coltrane
Jo Jo Calypso by Jim Nadel
Shoshana by Mark Levine
Sonnymoon for Two by Sonny Rollins
Tenor Madeness by Sonny Rollins
II.
Alright, Okay, You Win by Mayme Watts and Sid Wyche
Cold Duck Time by Eddie Harris
Doxy by Sonny Rollins
Equinox by John Coltrane
Jive Samba by Nat Adderly
Little Sunflower by Freddie Hubbard
Mercy, Mercy, Mercy by Josef Zawinul
Mr. P.C. by John Coltrane
Oye Como Va by Tito Puente
Revelation by Kenny Baron
Song for My Father by Horace Silver
Watermelon Man by Herbie Hancock
Work Song by Nat Adderly
III.
Blue Bossa by Kenny Dorham
Chameleon by Herbie Hancock
Gingerbread Boy by Jimmy Heath
Groove Merchant by Jerome Richardson
Killer Joe by Benny Golson
Perdido by Juan Tizol
Road Song by Wes Montgomery
Sister Sadie by Horace Silver
So Danco Samba by Antonio Carlos Jobim
St. Thomas by Sonny Rollins