In Java 8, you can use the new forEachRemaining method that's been added to the Iterator interface:

List<Element> list = new ArrayList<>();
iterator.forEachRemaining(list::add);

Example of each kind listed in the question:

ListIterationExample.java

import java.util.*;

public class ListIterationExample {

     public static void main(String []args){
        List<Integer> numbers = new ArrayList<Integer>();

        // populates list with initial values
        for (Integer i : Arrays.asList(0,1,2,3,4,5,6,7))
            numbers.add(i);
        printList(numbers);         // 0,1,2,3,4,5,6,7

        // replaces each element with twice its value
        for (int index=0; index < numbers.size(); index++) {
            numbers.set(index, numbers.get(index)*2); 
        }
        printList(numbers);         // 0,2,4,6,8,10,12,14

        // does nothing because list is not being changed
        for (Integer number : numbers) {
            number++; // number = new Integer(number+1);
        }
        printList(numbers);         // 0,2,4,6,8,10,12,14  

        // same as above -- just different syntax
        for (Iterator<Integer> iter = numbers.iterator(); iter.hasNext(); ) {
            Integer number = iter.next();
            number++;
        }
        printList(numbers);         // 0,2,4,6,8,10,12,14

        // ListIterator<?> provides an "add" method to insert elements
        // between the current element and the cursor
        for (ListIterator<Integer> iter = numbers.listIterator(); iter.hasNext(); ) {
            Integer number = iter.next();
            iter.add(number+1);     // insert a number right before this
        }
        printList(numbers);         // 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

        // Iterator<?> provides a "remove" method to delete elements
        // between the current element and the cursor
        for (Iterator<Integer> iter = numbers.iterator(); iter.hasNext(); ) {
            Integer number = iter.next();
            if (number % 2 == 0)    // if number is even 
                iter.remove();      // remove it from the collection
        }
        printList(numbers);         // 1,3,5,7,9,11,13,15

        // ListIterator<?> provides a "set" method to replace elements
        for (ListIterator<Integer> iter = numbers.listIterator(); iter.hasNext(); ) {
            Integer number = iter.next();
            iter.set(number/2);     // divide each element by 2
        }
        printList(numbers);         // 0,1,2,3,4,5,6,7
     }

     public static void printList(List<Integer> numbers) {
        StringBuilder sb = new StringBuilder();
        for (Integer number : numbers) {
            sb.append(number);
            sb.append(",");
        }
        sb.deleteCharAt(sb.length()-1); // remove trailing comma
        System.out.println(sb.toString());
     }
}