String.EMPTY is 12 characters, and "" is two, and they would both be referencing exactly the same instance in memory at runtime. I'm not entirely sure why String.EMPTY would save on compile time, in fact I think it would be the latter.

Especially considering Strings are immutable, it's not like you can first get an empty String, and perform some operations on it - best to use a StringBuilder (or StringBuffer if you want to be thread-safe) and turn that into a String.

Update
From your comment to the question:

What inspired this is actually TextBox.setText("");

I believe it would be totally legitimate to provide a constant in your appropriate class:

private static final String EMPTY_STRING = "";

And then reference it as in your code as

TextBox.setText(EMPTY_STRING);

As this way at least you are explicit that you want an empty String, rather than you forgot to fill in the String in your IDE or something similar.

Why on earth would you want a global variable in Java? James Gosling really tried to get rid of them; don't bring them back, please.

Either

0 == possiblyEmptyString.length()

or

possiblyEmptyString.isEmpty() // Java 6 only

are just as clear.

What's wrong with ""? It behaves like a constant, it's taken from the string pool and it's really short to write, much shorter than String.EMPTY.

Also, if what you need is to test if a string is empty, just do this:

myString.isEmpty();

UPDATE

If the string can be null, better use either isEmpty() or isNotBlank() from Apache Common's StringUtils class.

I use StringUtils.EMPTY, for hiding the literal and also to express that return StringUtils.EMPTY was fully expected and there should return an empty string, "" can lead to the assumption that "" can be easily changed into something else and that this was maybe only a mistake. I think the EMPTY is more expressive.