Well for many reasons, for instance the Singleton
pattern which some of the other members have pointed
out, but I use it to simulate in C/C++'s way of doing
const.

For instance, if I want to create a color object that
contains the Red, Green, and Blue values, I would have
to do this in Java.

public class Color
{
private int red;
private int green;
private int blue;

private Color( int red, int green, int blue )
{
this.red = red;
this.green = green;
this.blue = blue;
}

public Color RED = new Color( 255, 0, 0 );
public Color GREEN = new Color( 0, 255, 0 );
public Color BLUE = new Color( 0, 0, 255 );
public Color WHITE = new Color( 0, 0, 0 );
public Color BLACK = new Color( 255, 255, 255 );

// Public getter methods
public ...

// Do not include setter methods because we don't
want to change the object's data
}

So now I can do the following in other places

Color red = Color.RED;
Color black = Color.BLACK;