Wait, what's a Blossom Server?
Blossom Server is a fast, free, and easy to use multiplayer server built to host awesome multiplayer games. You can download the open source code and set up your own server, or you can create an account and use my free hosting.
Ok cool, how do I use it?
It's pretty easy. I'd start by downloading the Blossom Socket AS3 code, and then checking out the example included with it. For super detailed info, check out the reference page.
What are some other options?
Kongregate.com - Kongregate has some sort of multiplayer API, but only a select few are allowed to use it at the moment. It might be worth a shot to get in touch with them with your game idea.
Nonoba.com - Nonoba has a simple multiplayer system that is handily free.
Smartfoxserver.com - SmartFox is a widely used socket server written in java. They have several versions ranging all the way from free to kidney loss expensive.
Wowzamedia.com - The first I heard of Wowza was a couple of weeks ago. Dunno anything about it.
Chabotc.com - Something seems to have gone horribly wrong with the formatting of that page... Anywho... This is a nicely done socket server written in php. It's well suited for those of you who like to customize everything right down to the nuts and bolts.
Mmocha.com - MMOcha is a nice looking service for hosting multiplayer flash games. You have to partner with XGenStudios to use it.