Why does RuntimeException not require an explicit exception handling?

In general, there are two ways to handle exceptions in Java.

1. Add throws declaration in method signature
2. Surround with try/catch block.

However, I've noticed that some exceptions, especially the ones that inherit from RuntimeException, do not require such explicit exception handling.

For example, I created a sample method as below and marked "Not required" for the ones that do not require explicit exception handling.

public void textException(){
    int i = (new Random()).nextInt(100);

    switch (i){
    case 1:
        throw new NullPointerException();   //Not required
    case 2:
        throw new NumberFormatException();  //Not required
    case 3:
        throw new RuntimeException();       //Not required
    case 4:         
        throw new ClassNotFoundException(); //Required
    case 5:
        throw new IOException();            //Required
    case 6:
        throw new Exception();              //Required
    default:
        return;
    }
}

I noticed that RuntimeException inherits from Exception.

Why is it that RuntimeException does not need to be explicitly caught to be compiled whereas other Exceptions do?