I am using the SP2010 Client Object Model to upload to a document library, following the lead from Microsoft here: http://msdn.microsoft.com/en-us/library/ee956524.aspx#SP2010Cl
Soledad Pano has a blog-entry Sharepoint Upload File Error: ‘The remote server returned an error: (409) Conflict’, which helped me:
I figured out that the problem was the library name. It contained a dash on it, like “My-LibraryName”. When I renamed it without the dash it started working