I was trying to save a file without an extension from Notepad. For some reason, even if I removed the extension from the filename and selected "All files", it still saved as a .txt.
The trick turned out to be putting the file name in quotes. So for example, rather than saving the file as filename (which results in a file named filename.txt) I needed to save it as "filename" (which results in filename — removing the quotes but not adding the extension).