While-loop in Java not working

Wrap all your blocks including if blocks in curly braces!

This:

if (foo) 
  doSomething();
  doSomethingElse();

is not working as you think it is as it's behaving as

if (foo) {
  doSomething();
}

doSomethingElse();

Instead wrap all blocks in curly braces so that there is no doubt:

if (foo) {    
  doSomething();
  doSomethingElse();
}

This looks like a learning exercise, so I'll give you a few hints rather than tell you outright.

1. In your IDE of choice, tell it to auto-indent your code. Look closely at where the if statement and its results fall.

2. Think carefully about what nextInt() does and about where and how often you want to call it.

You are calling input.nextInt() twice in the loop, only printing one of them. In effect, that is like skipping every other number in the input. Change your code to store the next input into a variable, then check the variable. I suspect this isn't your actual code as without setting notZero to false as a result of checking the condition, it will only execute the loop once. FWIW, notZero is a lousy variable name. It should be semantic, not indicate its expected value. You'll also want to only print the input value if it isn't the end of input indicator.

Scanner input = new Scanner(System.in);

System.out.println("Alright, what?");

boolean endOfInput = false;

while (!endOfInput) {
   int next = input.nextInt();

   if (next == 0) {
      System.out.println("End of sequence");
      endOfInput = true;
   }  
   else {
      System.out.println(next);
   } 
}

Your problem is here:

 if (input.nextInt() == 0)

When you call nextInt() twice it removes two numbers. You need to only call it once per iteration.

 while (notZero)  
 {
    int num = input.nextInt();
    System.out.println(num);

    if (num == 0) {
        System.out.println("End of sequence");
        notZero = false;    
    }

  }

Fix that along with the problem that Hovercraft Full of Eels pointed out and you should be good.

You're calling nextInt() twice each time through the loop. That means that each time around, you'll consume two numbers, doing different things with each one -- i.e., the one you print and the one you compare to 0 are two different numbers. You need to call nextInt() just once and store the result in a variable, then operate on it.

Besides the two reads inside your loop, I assume you want to have a block after your if-statement

if (input.nextInt() == 0) {
    System.out.println("End of sequence");
    notZero = false;    
}

Far as i see, notZero's only purpose is to terminate the loop. You don't need it if you use a loop that terminates on the loop condition. You also don't need to print the "End of sequence" inside the loop, since by definition, it prints once the sequence is ended.

If we test for the condition directly instead,

int n;
while ((n = input.nextInt()) != 0)
{
    System.out.println(n);
}
System.out.println("End of sequence");

You could also say for (int n = input.nextInt(); n != 0; n = input.nextInt()) instead of the while. It ensures that n is only visible within the loop, but it also means repeating yourself -- and leaving open the possibility that someone could make the two 'initialization' and 'increment' sections different later.