That's an interesting question, I hope this thread get some traction; as it is one I've asked periodically throughout my years working with Joomla. It's also a topic I feel which can provide insights to all levels of programmers.
When I asked a far more experienced programmer the same question, he said Joomla has lots of examples of hybrid and loose implementation with a few pure examples.
Now for my two sense!
MVC Architectural Pattern - probably most popular paradigm for structuring an application and its files for software development currently.
Command Pattern - The JHtml::_ and JText::_ classes resemble this pattern, although I'm not well versed on its official class diagram and would appreciate any insights.
Registry Pattern & Abstract Factory Pattern - An example of a hybrid approach I mentioned earlier in my opinion, in that the intent mimics the patterns but execution doesn't follow UML to the letter. JFactory would be the class which I'm referencing.
Strategy Pattern - A good example of this would be how JDatabase abstract factory handles implementation of database drivers through separation of concerns.
Now that you have peeked my interest on this topic again I will try and do some more research and hope other more knowledgeable developers can provide insights, corrections or clarity!