There are loads of different design patterns used, but there are a few obvious ones:
Proxy - used heavily in AOP, and remoting.
Singleton - beans defined in spring config files are singletons.
Template method - used extensively to deal with boilerplate repeated code (such as closing connections cleanly, etc..). For example JdbcTemplate, JmsTemplate, JpaTemplate.
There are loads of different design patterns used, but there are a few obvious ones: Proxy - used heavily in AOP, and remoting. Singleton - beans defined in spring config files are singletons by default.
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.
Proxy pattern may or may not be used in AOP, it depends on the implementation but yes for Spring it is used. Same goes for singletons, Spring beans may or may not be singletons and spring beans being singleton has nothing to do with AOP. You can even say that AOP is like Decorator design pattern. But more than design patterns, AOP is about the issues it solves. It gives you a way to handle cross cutting concerns...