I'll try my hand.
There's 9x17, which has also been called 9mm Police, 9mm Kurtz, and is now commonly known as .380. ~90-95gr. Famous guns chambered for the round include the PPK, Sig P230. Infamous guns include pretty much anything you'll find in a pawnshop under $150. Not bad, but there are better alternatives for self-defense.
You've got 9x18, also known as 9mm Makarov. Used in Maks, P64's and CZ82's. A hot ~95-100gr round that's a bit better than .380 for penetration. There used to be alot of milsurp ammo for it, but it's getting harder to find.
9x19, which is also known as Parabellum or Luger (I love asking people "Parabellum or Luger?" when they ask for a "box o' nines.") The most widely used cartridge on earth. 95-147gr bullets, can be loaded to high pressures, and is cheap and available in too many loadings and brands to list. A true defensive cartridge. Most modern companies have at least one flagship gun chambered for it.
9mm Largo is an older Spanish cartridge from the turn of the 20th century that saw a brief resurgence in popularity in the 1980s. Alot of Stars and Astras were built for the cartridge. Not sure of the ballistics, but it inspired the 9x23.
9x21 is an Italian oddball. I once saw it used at a match. Same loadings as 9x19, but with a longer case. Performance is said to be similar. I don't know of any commercially available guns chambered for it.
9x23. Ahhh...this is where it gets fun! ~1430fps in 124gr loadings. This is what .357SIG should've been (not that it's a bad round, but...). A friend has a 1911 chambered for it, and it's a great round. Flat trajectory, good velocity, mild recoil. Some claim it's as effective as .357 Magnum against little furry critters. There's a good article on it
here.
Hope this helps. I'm sure some other folks have more experience with the rarer ones than I do, so I look forward to reading them. Actually, if we want to compile a faq, I'd be glad to host it.
I WANT a nice 9x23 autoloader, but ammo's a bit hard to find.