Reading Coding Horror’s post about Defining Open Source I only come to know that there are [tag]blogware[/tag] written in .NET platform and is ‘open source’ whatever that may mean to you.
These are DasBlog, BlogEngine.NET and SubText. These are all written in C# which I don’t know about. Are they popular, I can’t say but as far as what I have seen they aren’t popular probably due to the language barrier and hosting requirements. I’ll include these rare species into my collection here about blogware.