The .azw files are identical to MOBI (.mobi or .prc). If any ebook is DRM-free (not encrypted), Calibre can convert it to MOBI for you and the result will be readable on the Kindle.
The Kindle also reads text files and PDFs, and you can email some other formats to Amazon for conversion.
See
Kindle HowTo: File Conversion. I suggest Calibre over these options, but they all work (and all convert documents to the MOBI format).