How do I clear all options in a dropdown box?

Probably, not the cleanest solution, but it is definitely simpler than removing one-by-one:

document.getElementById("DropList").innerHTML = "";

If you wish to have a lightweight script, then go for jQuery. In jQuery, the solution for removing all options will be like:

$("#droplist").empty();

To remove the options of an HTML element of select, you can utilize the remove() method:

function removeOptions(selectElement) {
   var i, L = selectElement.options.length - 1;
   for(i = L; i >= 0; i--) {
      selectElement.remove(i);
   }
}

// using the function:
removeOptions(document.getElementById('DropList'));

It's important to remove the options backwards; as the remove() method rearranges the options collection. This way, it's guaranteed that the element to be removed still exists!