According to the book Laravel Design Patterns and Best Practices:
Chapter 5: Design Patterns in Laravel
- The Builder (Manager) pattern
- The need for the Builder (Manager) pattern
- The Factory pattern
- The need for the Factory pattern
- The Repository pattern
- The need for the Repository pattern
- The Strategy pattern -The need for the Strategy pattern
- The Provider pattern
- The Facade pattern
And let's not forget the Architectural Model-View-Controller Pattern.
I am not sure if all of these are used, but the book shows some examples of how to use them and if they are used, the examples are from the framework itself.
This book is for Laravel 4 though, so for an update, you have to ask Taylor Otwell.