How can I give control back (briefly) to the browser during intensive JavaScript processing?

Here is a solution:

function appendToSelect() {
  $("#mySelect").children().remove();
  $("#mySelect").html(
    '<option selected value="'+obj.data[0].value+'">'
    + obj.data[0].name
    + '</option>'
  );
  obj.data.splice(0, 1); // we only want remaining data
  var appendOptions = function() {
    var dataChunk = obj.data.splice(0, 10); // configure this last number (the size of the 'chunk') to suit your needs
    for(var i = 0; i < dataChunk.length; i++) {
      $("#mySelect").append(
        '<option value="' + dataChunk[i].value + '">'
        + dataChunk[i].name
        + '</option>'
      );
    }
    if(obj.data.length > 0) {
      setTimeout(appendOptions, 100); // change time to suit needs
    }
  };
  appendOptions(); // kicks it off
}

Not as elegant as @Borgar's solution, but you get the idea. Basically, I am doing the same thing, but all in your one function rather than breaking it into a higher-order function like he does. I like his solution, but if you don't, perhaps this will work for you.

EDIT: For those that don't immediately see it, one of the main differences between this solution and @Borgar's is that this solution allows you to set the size of the 'chunks' of data that is processed between each timeout. @Borgar's times-out after every single member of the array is processed. If I get time, I will try to create a higher-order function to handle this so it is more elegant. No promises though! ;)

EDIT: So, here is my adaptation of @Borgar's solution, which allows for setting a 'chunk' size and configuring the timeout value more easily:

function incrementallyProcess(workerCallback, data, chunkSize, timeout, completionCallback) {
  var itemIndex = 0;
  (function() {
    var remainingDataLength = (data.length - itemIndex);
    var currentChunkSize = (remainingDataLength >= chunkSize) ? chunkSize : remainingDataLength;
    if(itemIndex < data.length) {
      while(currentChunkSize--) {
        workerCallback(data[itemIndex++]);
      }
      setTimeout(arguments.callee, timeout);
    } else if(completionCallback) {
      completionCallback();
    }
  })();
}

function appendToSelect() {
  $("#mySelect").children().remove();
  $("#mySelect").html(
    '<option selected value="' + obj.data[0].value + '">'
    + obj.data[0].name
    + '</option>'
  );
  obj.data.splice(0,1); // we only want remaining data      
  incrementallyProcess(function(data) {
    $("#mySelect").append(
    '<option value="' + data.value + '">'
    + data.name
    + '</option>'
   );
  }, obj.data, 10, 100, removeAnimatedGifFunction); // last function not required...
}

Hope that helps - I think this combines the best of both solutions. Notice, the second anonymous function no longer uses the index value, but simply passes in the entire object (with the value and name properties); that makes it a bit cleaner, since the index of the current object really isn't usually that useful when iterating over things, IMO.

I am sure there are still things that could be done to make this even better, but that is left as an exercise for the reader. ;)

It just so happens that I was posting about this a moment ago here. Here is a timed loop function:

function processLoop( actionFunc, numTimes, doneFunc ) {
  var i = 0;
  var f = function () {
    if (i < numTimes) {
      actionFunc( i++ );  // closure on i
      setTimeout( f, 10 )
    } 
    else if (doneFunc) { 
      doneFunc();
    }
  };
  f();
}

For your situation this would be used like this:

function appendToSelect () {

  $("#mySelect").children().remove() ;
  $("#mySelect").html(
      '<option selected value="' + obj.data[0].value + '">'
      + obj.data[0].name
      + '</option>'
  );
  var j = 1 ;

  processLoop(function (i){
    $("#mySelect").append(
        '<option value="' + obj.data[i].value + '">'
        + obj.data[i].name
        + '</option>'
    ); 
  }, obj.data.length);

}

You'll want to make sure that you have a closure or some other access to the obj variable within the iteration function.

Hope this helps.