jQuery.fn.bindAndCall(type, callback): Not only bind a handler to an event, but also call it immediately once.

jquery.bindAndCall.js

/*!
 * Not only bind a handler to an event, but also call it immediately once.
 * @param {string} event  One or more event types separated by spaces. Only first listed will be immediately called.
 * @param {function(Object)} callback  The event handler
 * @returns {jQuery}
 */
jQuery.fn.bindAndCall = function(type, callback){
	this.bind(type, callback);
	var types = type.split(/\s+/); //because only one type makes sense to call
	this.each(function(){
		var event = $.Event(types[0]); 
		event.target = this;
		callback.call(this, event);
		return !event.isImmediatePropagationStopped();
	});
	return this;
};

I also added support for event.stopImmediatePropagation()