If null is a reasonable input parameter for your method, fix the method. If not, fix the caller. "Reasonable" is a flexible term, so I propose the following test: How should the method hande a null input? If you find more than one possible answer, then null is not a reasonable input.

For starters...the safest way to compare a String against a potentially null value is to put the guaranteed not-null String first, and call .equals on that:

if("constantString".equals(COMPLETEDDATE)) {
    // logic
}

But in general, your approach isn't correct.

The first one, as I commented, will always generate a NullPointerException is it's evaluated past country[23] == null. If it's null, it doesn't have a .length property. You probably meant to call country[23] != null instead.

The second approach only compares it against the literal string "null", which may or may not be true given the scope of your program. Also, if COMPLETEDDATE itself is null, it will fail - in that case, you would rectify it as I described above.

Your third approach is correct in the sense that it's the only thing checking against null. Typically though, you would want to do some logic if the object you wanted wasn't null.

Your fourth approach is correct by accident; if COMPLETEDDATE is actually null, the OR will short-circuit. It could also be true if COMPLETEDDATE was equal to the literal "null".

Assign null

When we write:

String s = "Hello World!";
s = null;

The String object still exists in memory because this does not delete it. However the garbage collector will clear the object from memory as there is no variable referencing it.
For all practical purposes s = null; deletes the String.

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.

First let's clarify something: You mention that after assigning null to the variable you could forget to initialize it, but by assigning null to it you are in effect initializing it.

public static void main (String args[]){
    String s;       
    System.out.println(s); // compiler error variable may not be initialized
}

vs

public static void main (String args[]){
    String s=null;      
    System.out.println(s); // no compiler error
    System.out.println(s.equals("helo")); // but this will generate an exception
}

So after you do String s=null; there's is no way that you could forget to initialize because you did initialize it.

That being clear, I would recommend you to use a "smart default". In your case perhaps the empty string "" would be a good default value if you want to avoid NullPointerException. In the other hand, sometimes it is desirable that the program produce an exception because it indicates something wrong happened under the hood that should not have happened.