While the Kindle Fire might be great for consuming content in Amazon's ecosystem, it only supports MP4 and VP8 video files. If you have a more diverse library, the latest update to Miro (the free media player / encoder) has you covered with support for Amazon's tablet. After installing on a Mac, Windows, or Linux machine, users can plug their device in, drag and drop video files to the icon in Miro's sidebar, and the video will encode and transfer to the device.
The only real catch seems to be that videos appear under the "Gallery" tab rather than the "Video" tab, which is reserved for content purchased on the Kindle Fire itself. Otherwise, this looks like a simultaneously simple and versatile solution for encoding video, and it also functions well as an alternative to iTunes for playing and managing your media. Kindle Fire users aren't the only ones who might be interested — Miro supports iOS, Android, and the Sony PSP as well.