I understand the scoping issue here, but the recursive solution is just all around better:

  function countdown(num) {
      if(num < 0) {
          return;
      }
      setTimeout(function() {
          alert(num);
          countdown(num - 1);
      }, 1000);
  }

Note: I'm aware that the dropbox version shows the first alert without any delay, whereas this waits a second before showing anything. This is slightly different behavior, but arguably acceptable.