Special thanks to Mark for this subject. Thanks Mark!
Collections are stored on Amazon
When you create a new collection, Amazon saves your collection. It will appear in Archived Items on other Kindles registered to your Amazon.com account. You can transfer collections across registered Kindles. This includes "real" Kindles only. Additional devices (like the iPad and Kindle for PC and Mac apps) don't support collections yet (darn it).
I believe this also means, if you lose your Kindle to an accident or something, and need to replace it, You should see your collection from the old Kindle in the Archives when you begin setting up the new one. You should be able to transfer the collection to your new Kindle.
special note: this will probably not work if you deregister the old/damaged Kindle. Wait until your collection is safely transferred to the new one before you do this. I looked in the Archives from my Kindle DX and was easily able to see the collections from my daughter's Kindle and my neice's, but not the DX I was holding in my hand.
How to get your collections back?
After poking around in the Kindle forums a bit, I discovered (but can't verify personally) a way to restore your collections if you lose the contents of your Kindle and then restore them from a backup on your computer. According to several posters, you can deregister your Kindle from your account, then register it again and the collections will appear.
I don't know that I would risk trying this on a Kindle with several hundred books and quite a lot of time invested in setting up your Collections. What I'm trying to say is do not try this at home just for fun. It could turn out to be very UN-fun.
