There are many good answers here, so let me offer another way to look at it...
There is no overkill when you are coding. It doesn't cost you anything to type @override, but the savings can be immense if you misspelled a method name or got the signature slightly wrong.
Think about it this way: In the time you navigated here and typed this post, you pretty much used more time than you will spend typing @override for the rest of your life; but one error it prevents can save you hours.
Java does all it can to make sure you didn't make any mistakes at edit/compile time, this is a virtually free way to solve an entire class of mistakes that aren't preventable in any other way outside of comprehensive testing.
Could you come up with a better mechanism in Java to ensure that when the user intended to override a method, he actually did?
Another neat effect is that if you don't provide the annotation it will warn you at compile time that you accidentally overrode a parent method--something that could be significant if you didn't intend to do it.