People put linux on their flash drives all the time. They also get hackintosh on their hard drives quite often. However, it'd be nice to be able to get the same live experience we get with Linux using OS X. With a distribution of OS X 10.6.2 called iPortable Snow, we can.
You'll need an actual Mac to create the thumb drive (some Hackintoshes may work; mine didn't). Search your favourite torrent site for iPortable Snow and download it. While it's downloading, format your external hard drive or thumb drive. Open up Disk Utility and select the drive you want to put OS X on. Go to the Partition tab and create one partition, formatted as Mac OS Extended (Journaled). Hit Options and make sure you're using the Master Boot Record option. Then hit Apply to format the drive.
Now you're done with Disk Utility, so go ahead and close it. Now, open the iPortable Snow installer you downloaded. You should get a window like this:
Double click the icon with the umbrella labelled "iPortable_Snow_x86". That should automatically open a program called CopyCatX, which will look like this:
In the first window, head to the Backup or Restore section, change the selected partition to the one you formatted for your Hackintosh, and click the Backup/Restore button.
In the next window, click the radio button on the right to change it so that you're restoring the drive to a backup. Then hit Start. It'll ask you to find a file to restore from. Use the "iPortable_Snow_x86" volume archive file on the iPortable Snow disk image. It will start copying the files to your thumb drive.
Next, you'll have to fix the bootloader. After it's done restoring, go back to the iPortable Snow Install folder. Open "First Aid". In there, you'll find a program called iPortable Bootfix. Open it. Continue through it normally, but on the third page, click "Change Install Location" (this is very important). You need to change that to your thumb drive. Otherwise, it'll install a new bootloader on your Mac that will break it. Once it finishes, you're done. Go ahead and rename the hackintosh partition whatever you like for the sake of personalisation.
You should now be able to boot from your thumb drive just like you would a live Linux thumb drive. Instead of booting into your computer's OS, you'll get the Chameleon screen with a few choices. iPortable Snow is designed to work on most Intel-based computers, though some video cards won't have advanced features (like 3D gaming) out of the box.
Ed. Note: While Will tested this on a few different Intel computers with great success, I could not get it to work on my Hackintosh at home (and sadly, the rest of my friends have Macs, with which iPortable Snow is ironically not compatible). So, if you have some time, give this a shot and let us know how it goes in the comments.