It's common knowledge that the Amazon Kindle Fire will only run apps approved by Amazon aka apps downloaded from the Appstore, but it looks like all that is about to change. Some folks have discovered that it's possible to sideload apps onto the tablet via a little “tweaking” of the tablet. No rooting is necessary, and the process seems simple enough but there's a chance that Amazon might disable the ability in a future update.
Ubergizmo, Amazon Kindle Fire allows sideloaded apps