Let's talk about formatting in terms of file type, and take something that is common on a computer as an example: pictures.
Pictures (or graphics files) come in literally dozens of files types, which can usually be determined by the file name extension; e.g., .jpg, .gif, .bmp, etc. Nowadays, most applications where you would view pictures can handle any of these file types, but ten years ago that was NOT the case. I remember owning graphic converting software that I had to use all the time. Word wouldn't take .jpg, only .gif, that kind of thing.
So, when you download an e-book from somewhere besides Amazon, there is a good likelihood that the file type extension will not be .azw or .azw1, which the Kindle can read natively. From our collective experience, the .azw files are always formatted in a way that throughout the book the fonts appear consistent and the line spacing is consistent and the widths of the paragraphs are consistent. The .azw1 files do not appear to be formatted properly, sometimes the fonts are skewed, and the paragraphs widths change all over the place, making it difficult to read. At this time, there is nowhere on the Amazon descriptions of the Kindle e-books that says whether the file is in format .azw or .azw1, so I recommend downloading a sample before actually purchasing any book.
As for free books from other websites, the file type is usually indicated on the webpage you download it from. If not, you can usually determine the file type after download by right-clicking on the file and choosing Properties. From there you may need to convert the file to a file type that the Kindle can read prior to transferring it to the Kindle via the USB connection. We will definitely get a definitive guide to converting file types posted soon.