The song I remember goes: "Call Roto Rooter, that's the name, and away goes trouble down the drain!"
Maybe it is because this is what I think of when I hear the word "rooter", that I say 'rowter' for "router".
I do think it interesting that so many people on the poll answered Root-Rowter. You would think most people would say either Root-Rooter or Rowt-Rowter.