[By the way, there are two tunes called Vine Street Drag. I am referring to the one by W. Howard Armstrong. The other (by J. Brown) is essentially the 32-bar main theme of Tiger Rag.]
There's a large repertoire of really good 16-bar tunes that bands don't play often enough, in my opinion. Some are particularly good for jazz effects, as they allow for 'breaks'. Think of Do What Ory Say or Up Jumped the Devil or If It Don't Fit, Don't Force It or Don't Go Away, Nobody or How Come You Do Me Like You Do or Hot Nuts, Get 'Em from the Peanut Man or Walkin' The Dog or Winin' Boy Blues or You've Got To See Mamma Ev'ry Night or Oh Miss Hannah, or Satan Your Kingdom Must Come Down or Rip 'Em Up Joe or Jamaica March or Walking With The King or I'm Watchin' The Clock.
Some of the 16-bar tunes are given an additional two-bar tag at the end (virtually repeating the final two bars). This can happen on the final chorus only or (as in My Sweet Lovin' Man and It's Right Here For You and I Wish I Could Shimmy Like My Sister Kate) on every chorus.
In a later stage of traditional jazz development, we find Chris Barber in 1959 producing Hush-a-Bye - a delightful minor key tune of 20 bars.
There's a lovely 24-bar song by Georgia White and Richard M. Jones. It's called I'm Blue and Lonesome (Nobody Cares for Me). You can find it performed exquisitely on YouTube by Tuba Skinny. The Chorus of Over in the Gloryland also comprises 24 bars. So does the Chorus of Sing On - and the Chorus of Tailgate Ramble. And I'm Coming, Virginia. And there are plenty of 24-bar blues (essentially a 'doubling up' of the 12-bar blues chord progression). Also there was a fashion in the first two decades of the Twentieth Century for songs that had VERSES of 24 bars, even though the better-known CHORUS had a conventional 32 bar-structure. Examples are San and I'm Forever Blowing Bubbles.
An interesting curiosity is the haunting Goodnight My Love, which could have sounded fine as a 32-bar tune (16 + 16) but which has an extra four bars inserted (starting at bar number 25), making it an even more emotional 36-bar tune.
There once was even a fashion for 40-bar tunes (essentially 10 batches of four bars). Think of Somebody Stole My Girl, If You Were the Only Girl in the World, Toot Toot Tootsie Goodbye, Sailing Down the Chesapeake Bay, and Cakewalking Babies from Home.
The lovely French tune La Mer (though rarely attempted by traditional jazz bands) uses the conventional a - a - b - a structure but substitutes 12 bars for the usual 8 in each section, with the result that it runs out at a very unusual 48 bars instead of the usual 32. And Cole Porter's Samantha uses 48 bars in an interesting way: essentially there is what could be a complete 32-bar tune [16 + 16] but Cole Porter then adds a further 16-bar theme.