How to move out of auto-completed brackets in IntelliJ IDEA (without using the arrow keys)?

IDEA doesn't have such feature yet. The closest equivalent is the Complete Current Statement editor action (Ctrl+Shift+Enter).

UPDATE

Initial implementation for this feature is available in 2018.2 EAP version - press Tab to jump out.

It works more like in MS Visual Studio - without visual indication of tab 'exit' position. For now, it should work in Java, SQL, Python and some other files. It will take some time for other languages to catch up - some language-specific code changes are required.

The feature is disabled by default, you can enable it in

Settings -> Editor -> General -> Smart Keys -> Jump outside closing bracket/quote with Tab

Ctrl + Shift + Enter does not seem to work for me in IDEA 12.1.4, but I found the closest feature to what I was looking for was Shift + Enter. This completes the line, creates a new line below the current line and moves the cursor to it.

You can do this by pressing the closing symbol that you would've pressed otherwise, but was auto completed. For example, if you have just typed the f below, you would press shift and 0 (or closing parenthesis), and it will move your cursor outside of the parenthesis.

String asdf = "hello world";
System.out.println(asdf);