What are the different design patterns used in Magento?

Factory:
It implement the concept of factories and deals with the problem of creating objects without specifying the exact class of object that will be created.

1 $product = Mage::getModel('catalog/product');

Singleton:

It restricts the instantiation of a class to one object. It will refer to same object each time called.
1 $category = Mage::getSingleton('catalog/session');

Registry:

It is a way to store information throughout your application.
Mage::register('key',$value); //stores
$currentCategory = Mage::registry('key'); //retrives

Prototype:

It determines the type of object to create. In Magento it can be Simple, Configurable, Grouped, Bundle, Downloadable or Virtual types.

Mage:getModel('catalog/product')->getTypeInstance();

Observer:

It is mainly used to implement distributed event handling systems. Here the subject maintains a list of its dependents, called observers, and notifies them automatically of any state changes, usually by calling one of their methods.

Mage::dispatchEvent('event_name', array('key'=>$value));
<config>
    <global>
        <events>
            <event_name>
                <observers>
                    <unique_name>
                        <class>Class_Name</class>
                        <method>methodName</method>
                    </unique_name>
                </observers>
            </event_name>
        </events>
    </global>
</config>

Object Pool:

It is used to reuse and share objects that are expensive to create.
$id = Mage::objects()->save($object);
$object = Mage::objects($id);

Iterator:

It is used to traverse a collection and access the collection’s items.
Mage::getModel('catalog/product')->getCollection();

Lazy Loading:

It is used to defer initialization of an object until the point at which it is needed.
$collection_of_products = Mage::getModel('catalog/product')
->getCollection();

Helper:

Multiple methods are available for use by other objects. Here you can use core’s helper methods from anywhere in the application.
Mage::helper('core');

Service Locator:

Allows overrides or renamed physical resources (e.g. Classes, DB tables, etc)
Mage::getModel('catalog/product') and $installer->getTable('customer/address_entity');