Inversion of Control
If you are ever going to design decoupled systems, you will need to know how to properly link dependencies between classes.
Command Pattern and Variants
In Java in particular, it is essential to learn how to pass a piece of functionality to another method as an object because of the lack of closures and function pointers in the language.
Factory Pattern
Factories are ubiquitous in Java frameworks and it is essential to learn why and when to use the factory pattern.
Singleton (pattern and anti-pattern)
Learning how to use the singleton pattern responsibly is very helpful for understanding the pitfalls in other people’s code you may be reading.
Overall, learning the why with regards to patterns is much more important the the how. Knowing when not to apply a pattern is just as important as knowing when to.