Markdown and reStructuredText (ReST) are two heavily used markup languages on the WWW. While I would have expected at first that the markup language from Wikipedia to spread due to the high popularity of the web site, it is actually two other ones which became successful.
Markdown is heavily used in the blog world, while ReST comes from the Python world. However, Markdown suffers from fragmentation and incompatibility in implementations, while ReST as a good specification and hooks for extensions.
I personnaly highly prefer RST. The following page will compare both markup syntaxe with a highly subjective point of view in flavor of ReST.