Since I am using the MediaWiki extracts API, I never had to find/write my own Wikitext parser. However, I did run into a couple in my research that seemed relatively popular:
I'm sure if you did a bit more digging you could find a C# library that does this, or you could roll your own pretty easily using the others as a model.
- https://github.com/dcramer/py-wikimarkup (coverts wikitext to HTML using Python, would need to extract text with BeautifulSoup or something
- http://wiki.eclipse.org/Mylyn/Incubator/WikiText (also to HTML, but in Java)
- https://github.com/earwig/mwparserfromhell
I'm sure if you did a bit more digging you could find a C# library that does this, or you could roll your own pretty easily using the others as a model.