Knockout + bootstrap-tagsinput

bindinghandler.js

ko.bindingHandlers.tagsinput = {
	init: function(element, valueAccessor, allBindings) {
    var options = allBindings().tagsinputOptions || {};
    var value = valueAccessor();
    var valueUnwrapped = ko.unwrap(value);
    
    var el = $(element);
    
    el.tagsinput(options);
    
    for(var i = 0; i < valueUnwrapped.length; i++) {
    	el.tagsinput('add', valueUnwrapped[i]);
    }
    
    el.on('itemAdded', function(event) {
    	if(valueUnwrapped.indexOf(event.item) === -1) {
      	value.push(event.item);
      }
    })
    
    el.on('itemRemoved', function(event) {
    	value.remove(event.item);
		});    
  },
 	update: function(element, valueAccessor, allBindings, viewModel, bindingContext) {
    var value = valueAccessor();
    var valueUnwrapped = ko.unwrap(value);
    
    var el = $(element);    
    var prev = el.tagsinput('items');
    
    var added = valueUnwrapped.filter(function(i) {return prev.indexOf(i) === -1;});
    var removed = prev.filter(function(i) {return valueUnwrapped.indexOf(i) === -1;});
    
    // Remove tags no longer in bound model
    for (var i = 0; i < removed.length; i++) {
      el.tagsinput('remove', removed[i]);
    }

		// Refresh remaining tags
    el.tagsinput('refresh');
    
    // Add new items in model as tags
    for (i = 0; i < added.length; i++) {
      el.tagsinput('add', added[i]);
    }
  }
};

https://jsfiddle.net/kkspk0oq/3/

I've created a slightly improved version which also works, when you replace the bound array. You can find it in my fork.