An example implementation on $('selector').tap();

jquery.tap.js

(function($) {
  // DON'T EVER USE AN ALERT INSIDE THE CALLBACK.
  $.fn.tap = function(callback) {
    if (!this) return false;

    return this.each(function() {
        var element = this;

        if (element.touchHandler) { return; }

        element.touchHandler = {
          element: element,
          callback: callback,
          origin: { x: 0, y: 0 },
          destination: { x: 0, y: 0 },
          threshold: 4,

          withinThreshold: function(){
            // console.debug('destination.x: ' + destination.x + ' destination.y: ' + destination.y)

            var changeX = this.origin.x - (this.destination.x),
                changeY = this.origin.y - (this.destination.y);

            // console.debug("changeX: " + changeX + " changeY: " + changeY)

            withinY = changeY < this.threshold && changeY > (this.threshold*-1);
            withinX = changeX < this.threshold && changeX > (this.threshold*-1);

            // console.debug("withinX: " + withinX + " withinY: " + withinY)

            return withinY || withinX;
          },

          handleEvent: function (e) {
            if (e.type == 'touchstart') { this.touchStart(e); }

            if (e.type == 'touchmove') { this.touchMove(e); }

            if (e.type == 'touchend') { this.touchEnd(e); }

            if (e.type == 'touchcancel') { this.touchCancel(e); }
          },

          touchStart: function(event){
            // console.debug('touchStart')
            this.origin.x = event.targetTouches[0].pageX
            this.origin.y = event.targetTouches[0].pageY

            element.addEventListener('touchmove', this, false);
            element.addEventListener('touchend', this, false);
            element.addEventListener('touchcancel', this, false);
          },

          touchMove: function(event){
            // console.debug('touchMove')
            this.destination.x = event.targetTouches[0].pageX
            this.destination.y = event.targetTouches[0].pageY
          },

          touchEnd: function(event){
            // console.debug('touchEnd')
            element.removeEventListener('touchmove', this, false);
            element.removeEventListener('touchend', this, false);
            element.removeEventListener('touchcancel', this, false);

            var moved = (!!this.destination.x || !!this.destination.y);

            // console.debug('moved: ' + moved)

            if (moved && this.withinThreshold()) {
              // console.debug('tapped')
              this.callback.apply(this.element, arguments);
            }

            if (!moved) {
              // console.debug('tapped');
              this.callback.apply(this.element, arguments);
            }

            this.reset();
          },

          touchCancel: function(event){ this.reset(); },

          reset: function(){
            this.origin.x = 0;
            this.origin.y = 0;
            this.destination.x = 0;
            this.destination.y = 0;
          }
        };

        element.addEventListener("touchstart", element.touchHandler, false);
    });
  };
})(jQuery);