Files REQUIRE a file extension. In order to have an HTML file, your computer must recognize it as an HTML file. How do you think your computer recognizes files to be HTML and not something else? By the file extension (.html).
If you don't want to see the file extensions, open MyComputer, go to Tools at the top, and drop down to FolderOptions. Then go to "View" tab and play around with the correct check boxes. But no matter what you do, you won't be able to get the file extensions to go away (and still have a usable file at the same time).