Not sure I'm understanding this. .RM is a file extension for video to be played via Real Player. You double-click the file, it starts playing in Real Player. Are you saying EVERYTHING you download gets a .rm appended to the filename ?
If what you're downloading are .zip files, that's a different story. To get winzip to open these again, just right click the .zip file and choose OPEN WITH --> Choose Program --> Browse for Winzip (or winzip.exe) and choose it. ALSO select the checkbox that says "always use selected program to open this kind of file". That should correct the file association for .zip files for you.