First Concurrency Technique

In November 2009 I went to No Fluff Just Stuff. One of the presentations was by Brian Goetz, which was about Java concurrency. For some reason there were items on his agenda slide that were not covered in his presentation.

He went over some strategies, and at the end he pointed out a common tactic that he also said is a good rule of thumb for concurrency in Java: Make your variables private, and make any methods that access them synchronized.

That sounds pretty simple. And perhaps too good to be true. I will post on some forums and boards populated by people with more knowledge than me if there are situations/applications where this concurrency technique would not be sufficient. Would relying primarily on this technique work well in systems with lots of transactions, or large data sets? What are the potential drawbacks of doing this?

Image from Wikimedia, assumed allowed under Fair Use. Image from the Vatican Virgil, a 5th century manuscript of poems by Virgil.