I've done a potato, who hasn't? I've done a mango pit, which grew on the window sill of my upper-Broadway apartment for almost a year, then mysteriously died. And I've plunked celery in water (sometimes colored) and watched it suck up the nutrients while sprouting an up-do.
But sesame? Persimmon? Figs?
For those curious about the way the earth and it's bounty grows, a quick perusal through Don't Throw It, Grow It! by Deborah Peterson would be a fun way to start. Perfect for the urbanite with "no room for a garden" and great for children just beginning to get their little heads around the cycle of life.
Heck, I'm a fairly seasoned gardener and I think I just might cut back on the composting and just go straight to gardening with my scraps.
Don't Throw It, Grow It: 68 Windowsill Plants from Kitchen Scraps (Storey, May 2008)