Below are some reasons arguing for the use of the pattern and example code in Java, but it is an implementation of the Builder Pattern covered by the Gang of Four in Design Patterns. The reasons you would use it in Java are also applicable to other programming languages as well.

As Joshua Bloch states in Effective Java, 2nd Edition:

The builder pattern is a good choice when designing classes whose constructors or static factories would have more than a handful of parameters.

We've all at some point encountered a class with a list of constructors where each addition adds a new option parameter:

Pizza(int size) { ... }        
Pizza(int size, boolean cheese) { ... }    
Pizza(int size, boolean cheese, boolean pepperoni) { ... }    
Pizza(int size, boolean cheese, boolean pepperoni, boolean bacon) { ... }

This is called the Telescoping Constructor Pattern. The problem with this pattern is that once constructors are 4 or 5 parameters long it becomes difficult to remember the required order of the parameters as well as what particular constructor you might want in a given situation.

One alternative you have to the Telescoping Constructor Pattern is the JavaBean Pattern where you call a constructor with the mandatory parameters and then call any optional setters after:

Pizza pizza = new Pizza(12);
pizza.setCheese(true);
pizza.setPepperoni(true);
pizza.setBacon(true);

The problem here is that because the object is created over several calls it may be in an inconsistent state partway through its construction. This also requires a lot of extra effort to ensure thread safety.

The better alternative is to use the Builder Pattern.

public class Pizza {
  private int size;
  private boolean cheese;
  private boolean pepperoni;
  private boolean bacon;

  public static class Builder {
    //required
    private final int size;

    //optional
    private boolean cheese = false;
    private boolean pepperoni = false;
    private boolean bacon = false;

    public Builder(int size) {
      this.size = size;
    }

    public Builder cheese(boolean value) {
      cheese = value;
      return this;
    }

    public Builder pepperoni(boolean value) {
      pepperoni = value;
      return this;
    }

    public Builder bacon(boolean value) {
      bacon = value;
      return this;
    }

    public Pizza build() {
      return new Pizza(this);
    }
  }

  private Pizza(Builder builder) {
    size = builder.size;
    cheese = builder.cheese;
    pepperoni = builder.pepperoni;
    bacon = builder.bacon;
  }
}

Note that Pizza is immutable and that parameter values are all in a single location. Because the Builder's setter methods return the Builder object they are able to be chained.

Pizza pizza = new Pizza.Builder(12)
                       .cheese(true)
                       .pepperoni(true)
                       .bacon(true)
                       .build();

This results in code that is easy to write and very easy to read and understand. In this example, the build method could be modified to check parameters after they have been copied from the builder to the Pizza object and throw an IllegalStateException if an invalid parameter value has been supplied. This pattern is flexible and it is easy to add more parameters to it in the future. It is really only useful if you are going to have more than 4 or 5 parameters for a constructor. That said, it might be worthwhile in the first place if you suspect you may be adding more parameters in the future.

I have borrowed heavily on this topic from the book Effective Java, 2nd Edition by Joshua Bloch. To learn more about this pattern and other effective Java practices I highly recommend it.

I'm not sure about within the core JDK, but good examples can be found in Guava. MapMaker is probably the best example I can think of off the top of my head. For example, from the docs:

ConcurrentMap<Key, Graph> graphs = new MapMaker()
    .concurrencyLevel(32)
    .softKeys()
    .weakValues()
    .expiration(30, TimeUnit.MINUTES)
    .makeComputingMap(
        new Function<Key, Graph>() {
          public Graph apply(Key key) {
            return createExpensiveGraph(key);
          }
        });

Yes, this sort of thing can go against the grain of "standard" Java naming, but it can also be very readable.

For situations where you're not returning "this" but a new object (typically with immutable types) I like a "with" prefix - Joda Time uses that pattern extensively. That's not the builder pattern, but an alternative and related construction form.