Singleton - beans defined in spring config files are singletons by default.
Template method - used extensively to deal with boilerplate repeated code (such as closing connections cleanly, etc..). For example JdbcTemplate, JmsTemplate, JpaTemplate.
Update following comments: For MVC, you might want to read the MVC Reference
Some obvious patterns in use in MVC:
Model View Controller :-) . The advantage with Spring MVC is that your controllers are POJOs as opposed to being servlets. This makes for easier testing of controllers. One thing to note is that the controller is only required to return a logical view name, and the view selection is left to a separate ViewResolver. This makes it easier to reuse controllers for different view technologies.
Spring is a collection of best-practise API patterns, you can write up a shopping list of them as long as your arm. The way that the API is designed encourages you (but doesn't force you) to follow these patterns, and half the time you follow them without knowing you are doing so.
The DI thing actually is some kind of strategy pattern. Whenever you want to be some logic/implementation exchangeable you typically find an interface and an appropriate setter method on the host class to wire your custom implementation of that interface.
Factory Method patter: BeanFactory for creating instance of an object
Singleton : instance type can be singleton for a context
Prototype : instance type can be prototype.
Builder pattern: you can also define a method in a class who will be responsible for creating complex instance.
Spring container generates bean objects depending on the bean scope (singleton, prototype etc..). So this looks like implementing Abstract Factory pattern. In the Spring's internal implementation, I am sure each scope should be tied to specific factory kind class.
Service Locator Pattern - ServiceLocatorFactoryBean keeps information of all the beans in the context. When client code asks for a service (bean) using name, it simply locates that bean in the context and returns it. Client code does not need to write spring related code to locate a bean.