I would like to know about the design patterns that can be applied in Java EE 6 implementation.
Do JPA eliminate the use of DAO?
Please provide other patterns that can be learned.
If you use Java EE 6 (not Java EE 5), then some of technical J2EE patterns are not needed anymore for the task they are used in J2EE.
For example, use injection instead of ServiceLocator.
@See http://pawelstawicki.blogspot.com/2010/07/review-real-world-java-ee-patterns.html
GOF patterns still required, because they are not (only) related to Java EE.
In general: Patterns have an intend: they want to produce a solution/best practice for an problem, with a given set of functionality that is proviced by the environment (In your case: it is Java, Java EE 6, ...)