Here's the answer: they all will*. According to its Developers FAQ, Amazon is reviewing every single app in its Appstore to ensure compatibility with the Fire. That means all of the games, tool, and web-related apps you find will be perfectly by the time you get your device, and you can go ahead and start getting apps now.
What's that little asterisk for? Because the Fire has different specifications and capabilities, some existing apps will not function completely on the new device. This includes apps that require Google Mobil Services, a gyroscope, a camera, a microphone, Bluetooth, GPS, WAN module, in-app purchases, or a removable SD card. This does restrict some apps like Soundhound or others that might be hard to give up.
There are plenty of functions Fire Apps will have though, and I'll be very interested to see how developers stretch these to the limits on the new device. Fire Apps can make use of the web, multitouch input, the light censor, landscape and portraits modes, plus USB accessories.
One thing users will have to keep an eye on and let us know about is if they feel at all constricted because of these features. Of course, it's equally likely that many won't notice because they've got their hands full with plenty of things to read, play, and watch!
To summarize, all apps in the Amazon Appstore are fair game, but keep an eye out for any that might require the unusable features listed above. One thing you can be sure of though is that all apps available on Amazon from now on will adhere to the proper specifications, and this question of whether an app works for the Fire or doesn't will become a thing of the past.
Let's close with a useful free app that should be an automatic download for anyone waiting to get their device.
Name: Wifi Analyzer
Rating: 4.8 stars over 161 reviews
Description: Finding the best WiFi signal is often a challenge. Enter WiFi Analyzer, a helpful Android app that provides clear graphical views of the WiFi signals in your vicinity. WiFi Analyzer lets you choose the strongest wireless signal that has the least amount of traffic an interference.
Analysis: Considering the Kindle Fire is a WiFi only device, finding a good signal is a must and those little bars just don't tell the whole story. This app will give you the full details on up to five different signals and has plenty of customizable settings. Don't get shut out of the web!