We've chosen these because all of them work almost instantaneously, you just have to click on a button. However, if you're willing to put just a wee bit more effort into the customization of your avatar, you should check out our big list of online avatar creation applications.
TurnYourNameIntoAFace - this tool generates an avatar based on your name. Type in any name you like, and you get a unique, old school looking avatar (this is mine; not too shabby). Found via Labnol, this cute app has been created for the 24 Hour Application Challenge.
Simpsons Avatar - besides offering the ability to create customized avatars yourself, Simpsons avatar creator also has a randomize button (accessible via the dices button in the menu at the bottom of the page), which will randomly generate a Simpsons-style avatar for you.
Blockhead Iconizer - ever needed to create a LEGO-style avatar? Well, now you can. If you're too lazy to try out all the options, just click the ????? button and you'll get a randomly generated one. Be careful, though, the results might be too random for your taste. If you do it by hand, you'll probably get much better results.
Portrait Illustration Maker - here's another quite advanced avatar maker; advanced in the sense that it offers a huge number of gizmos and gadgets you can add to your avatar - silly hats, hotdogs, macbooks, it's all there. The big fat "Randomizer" button will save you the effort of actually trying to build an avatar and present you with a random one, often with solid results.
BuildYourWildSelf is a totally wacky avatar creation application with resulting avatars being odd at the very least. The cartoonish drawing style might appeal to you or scare you away, but the important thing is that it's possible to randomly generate an avatar so you can try out a few without putting much effort into it.