Here are some popular jazz standards for beginning improvisers. These tunes are well known and regularly played in jam sessions. They are great for learning how to improvise because they have fewer chord changes, a couple of tonalities and usually easy melodies.
10 Jazz Standards for Beginners
A medium tempo swinging tune written by pianist Fats Waller who famously interpreted his song for the movie "Stormy Weather" (1943). It has a classic AABA form going to the minor relative on the B section.
Autumn Leaves is a great standard to practice major and minor II V I progressions. It is most often played in Gm and Am.
Course : Autumn Leaves: Jazz Improv' Work Out
A simple but powerful melody in the key of D minor. This is a very popular standard by Victor Young.
A 16 bars tune written by Kenny Dohram. The main key is C minor and it goes to Db major during 4 bars on the bridge. If you know the Eb major and Db major scale you can already improvise over the form.
An old classic song that everyone should learn. The first motif is a perfect example of the pivot technique. After you have practiced Honeysuckle Rose you could learn Charlie Parker's composition "Scrapple From The Apple" which uses the same chord progression but with a bebop head.
Maiden Voyage is a modal tune by Herbie Hancock that follows the traditional AABA song form. You can use the myxolidian modes to blow over the various Sus (chords throughout the sections. A "Sus" chord (Sus for suspended) is a dominant chord with a fourth instead of a third. For ex D7(sus4) is D G A C
Miles Davis ' "So What" is a great vehicle to practice the D and Eb Dorian modes. Next you can learn the melody of "Impression" by John Coltrane which share the same chord progression.
Lesson: So What Improvisation
A classic standard written by George Gershwin for the opera" Porgy and Bess". It is usually played in D minor but you should lear it in different keys as well. It could come handy if you play with a singer.
Take The "A" Train
Billy Strayhorn is one of the greatest composer of the XX century. His composition "Take The "A" Train" based from the changes of "Exactly Like You" is a tune that you should know! It is most of the time played in C major.
A bluesy medium tempo tune in F minor with a bridge. You can improvise using the F minor pentatonic, F bebop minor scale, the C phrygian dominant scale and Bb melodic minor (bridge).