How to test a null String in JAVA?

string == null compares if the object is null. string.equals("foo") compares the value inside of that object. string == "foo" doesn't always work, because you're trying to see if the objects are the same, not the values they represent.

Longer answer:
If you try this, it won't work, as you've found:

String foo = null;
if (foo.equals(null)) {
    // That fails every time. 
}

The reason is that foo is null, so it doesn't know what .equals is; there's no object there for .equals to be called from.
What you probably wanted was:

String foo = null;
if (foo == null) {
    // That will work.
}

The typical way to guard yourself against a null when dealing with Strings is:

String foo = null;
String bar = "Some string";
...
if (foo != null && foo.equals(bar)) {
    // Do something here.
}

That way, if foo was null, it doesn't evaluate the second half of the conditional, and things are all right.
The easy way, if you're using a String literal (instead of a variable), is:

String foo = null;
...
if ("some String".equals(foo)) {
    // Do something here.
}

If you want to work around that, Apache Commons has a class - StringUtils - that provides null-safe String operations.

if (StringUtils.equals(foo, bar)) {
    // Do something here.
}

Another response was joking, and said you should do this:

boolean isNull = false;
try {
    stringname.equalsIgnoreCase(null);
} catch (NullPointerException npe) {
    isNull = true;
}

Please don't do that. You should only throw exceptions for errors that are exceptional; if you're expecting a null, you should check for it ahead of time, and not let it throw the exception.
In my head, there are two reasons for this. First, exceptions are slow; checking against null is fast, but when the JVM throws an exception, it takes a lot of time. Second, the code is much easier to read and maintain if you just check for the null pointer ahead of time.