Books you buy from the Kindle Store on Amazon, only work on Kindle (whether this is the Kindle device, or the various Kindle applications.)
However, you can purcahse books from other vendors (fictionwise, etc.) in Mobipocket format and read them on the device - you just have to load them using USB. (Note that it's only Mobipocket non-DRM books that you can read.)
Alternatively, the software Calibre can convert a wide range of (non-DRM) ebooks into the format the Kindle uses.
I have a mix of bought-from-Amazon ebooks , and books I've bought from other sources (and free ones from places like feedbooks). The only difference is, that I have to load 'em by USB, and the ones that aren't from Amazon aren't available for me to 'pull down from the cloud' .
