What could be causing this problem?
Have you checked that the actual site always returns documents with an extension? There is no protocol which requires this and it is completely normal to not use them; the document type is determined by the http headers and not any suffix on the address. Of course, your file browser does use file extensions to identify documents, so this may be an annoyance.
For example, this page is literally
http://unix.stackexchange.com/questions/124741/wget-corrupted-directories, and if you fetch it with
wget, it will produce a file
wget-corrupted-directories with no extension, which contains html data.