For a comprehensive explanation, more formats, and a table of supported devices please see the Wikipedia article Comparison of e-book formats.
Amazon Kindle (.azw, .azw1)
Proprietary format used only with Kindle devices and applications. Usually DRM protected.
Broadband eBooks (.lrf, .lrx, .lrs)
BBeB. Sony eBook format, discontinued in 2010.
Comic Book Archive ( cbr, .cbz, .cb7, .cbt, .cba)
Compressed folders of images. Stored using ZIP, RAR, 7z, TAR, or ACE archive types. Comic Book Archives are not a distinct file format, they are normal archives that have been given a different file extension. CBA reader applications are available for desktops, tablets and smart phones.
ePub (.epub)
Most widely supported format for eBooks. DRM protected or DRM-free. Established by the International Digital Publishing Forum (IDPF) The first version was developed in 1999, EPUB 3 was approved in October 2011.
eReader /PalmDOC (.pdb)
Developed by Palm Digital Media in 1996. Now uncommon. Was used by Barnes and Noble to distribute e-books but has been superseded by the ePub format.
FictionBook (.fb2)
Open XML based e-book format developed in Russia.
Microsoft Word Document (.doc, .docx)
Flexible and extensive text formatting used by word processing programs. .doc was Microsoft Word’s default file type which in use, in various iterations, since 1983. .docx became the Microsoft Word’s default file type in 2007 replacing the .doc extension. .docx uses XML and ZIP compression resulting in significantly smaller file sizes than .doc files.
Mobipocket (.prc, .mobi)
Older file format developed for smart phone mobile reading. Based on the first version of the ePub format (Open eBook). The development company was bought by Amazon in 2005. Amazon’s Kindle file format is derived from the .mobi format.
Plain Text (.txt)
The simplest format for digital text, no formatting is supported.
Portable Document Format (.pdf)
Industry standard for displaying and distributing formatted text. Supports images, tables, special characters and equations.
Rich Text Format (.rtf)
An upgrade from Plain Text, Rich Text was developed my Microsoft in 1987 and supports limited formatting.