I've heard of folks in warmer climates growing banana and papaya trees, but didn't think I could hope to do so here in Virginia.
But I happened across the GreenEarth website. He's got two dwarf banana varieties I could grow in my short greenhouse, and a third variety, California Gold, that should survive outside in the winters here (I'm in Zone 7a). Here's the description for the Truly Tiny Banana Plant, which I'm thinking of trying out:
Delightful small banana that has a beautiful form. Grows only to about 2 - 3 feet in height. Excellent houseplant. Great as a groundcover or as a container plant. Likes generally warm conditions, bright light, moist soil. Fast grower that quickly attains full size. A miniature version of the Dwarf Cavendish Banana. Grows only 24" tall. Great tasting bananas. Easy to grow, indoors or out! Zone 8-11. Great house or patio plant. approx. 6" to 8" plant.
Now that's sweet!