[bash] How to loop through a directory recursively to delete files with certain extensions

If you want to do something recursively, I suggest you use recursion (yes, you can do it using stacks and so on, but hey).

recursiverm() {
  for d in *; do
    if [ -d "$d" ]; then
      (cd -- "$d" && recursiverm)
    fi
    rm -f *.pdf
    rm -f *.doc
  done
}

(cd /tmp; recursiverm)

That said, find is probably a better choice as has already been suggested.