You can even find a few competitor's reading apps in the Amazon Appstore. For example, Kobo had their app in there since Amazon launched the Appstore, and the same goes for Aldiko. You can also find Wattpad, ReadItLater, Bluefire, and other reading apps.
Here's the interesting part: you cannot see most of those apps when browsing the Amazon Appstore from the Kindle Fire.
I've spent the morning double checking, and it looks like Amazon pulled a sleight of hand with the new Kindle Fire. I can confirm that Bluefire Reader, Kobo, Wattpad, and Aldiko cannot be found via the Kindle Fire. The apps are still there, and they will likely still work. But Amazon won't provide them to you. You'll need to find the app elsewhere.
Update: Wattpad just announced that their app is now available on the Kindle Fire. I cannot see it, and according to the listing page that app is not compatible with the Kindle Fire. I will update this post if that changes.
Now, what this usually means is that Amazon doesn't think the apps are compatible. I've encountered hidden apps with any number of Android tablets and usually Amazon is right; the apps won't work. But not in this case. I went looking and found several of the apps elsewhere. I can confirm that Kobo, Aldiko, and Wattpad work just fine on the Kindle Fire.
Second Update: I've just been told by Bluefire that their app had been tested for the KF when it was submitted to Amazon. Amazon told Bluefire that the app was compatible, so there's absolutely no reason for it to not be listed.
Amazon is hindering their competition from their tablet.
Pretty slick trick from Amazon, isn't it? Sure, they allow their competitors to upload an app to their app store, but that doesn't mean Amazon actually has to list it. And since none of the apps released by Amazon's direct competitors are listed for the Kindle Fire, it's going to be a kinda hard to install and use them.
Now, this is only beginning to bother me. I mentioned this is a footnote to a post this morning, and I didn't think it was important at the time because I could still install the apps. But now that I've seen how thorough Amazon was in blocking their competition and the underhanded manner in which they did it, it reminds me that Amazon is only pretending to be customer oriented. They won't hesitate to trick you if it suits their best interest.
On the other hand, I can still install apps found elsewhere, and that puts the Kindle fire a step above the Nook Tablet and the iPad. B&N doesn't even carry competing reading apps, and Apple is Apple. I'd say both are worse than Amazon in this regard.