public class Mememe {
   private static int m_AccessableInt; // доступно в StaticNestedMememe
   private int m_NotAccessableInt;     // не доступно в StaticNestedMememe
   [...]

   public static class StaticNestedMememe {
      [...]
   }
}

Mememe.StaticNestedMememe nestedObject = new Mememe.StaticNestedMememe();

public class Mememe {
    public void calc(String requestPath) {
        class Сalculator{
             int calc() { return 0; }
        }
    }
}

new Thread(new Runnable() {
        public void run() {
            ...
        }
    }).start();

public class OuterClass {
    public void method() { ... }

    public class InnerClass {
        public void method() { ... }

        public void anotherMethod() {
            method();
        }
    }
}

OuterClass outer = new OuterClass();
OuterClass.InnerClass innerClass = outer.new InnerClass();

public class Example {

    public static int si = 0;
    private static int psi = 0;
    public final Inner inner;
    public int i = 0;
    private int pi = 0;

    public Example() {
        inner = new Inner();
    }

    public static class Nested {

        int e;

        public Nested() {
            e = Example.psi;
            e = Example.si;
            // а вот так нельзя
//            e = Example.this.pi;
//            e = Example.this.i;
        }

    }

    public class Inner {
        int e;

        public Inner() {
            e = Example.psi;
            e = Example.si;
            e = Example.this.pi;
            e = Example.this.i;
        }
    }

}

class ExampleTwo {
    // Nested можно сразу
    Example.Nested nested = new Example.Nested();

    Example.Inner inner;
    {
    // так нельзя, нужен объект Example
//        inner = new Example.Inner();
        // а так можно
        Example example = new Example();
        inner = example.inner;
    }

}