How to multiply all values in an array?

The problem is that you don't keep track of how many items there are in the array that actually are assigned a value. If you exit from the loop using a zero input, then the rest of the items are unchanged. As they are zero by default, you will be using those zeroes in your second loop, and when you have a zero somewhere in the array, the total product becomes zero.

Keep track of how many items there are by keeping the loop variable outside the loop:

int input = 0;
while (input < SIZE)
{
    userInput = Console.ReadLine();
    numberInputed = int.Parse(userInput);
    if (numberInputed == ZERO) {
      break;
    }
    numbers[input] = numberInputed;
    input++;
}

Now you can use only the items that are actually assigned:

for (int i = 0; i < input; i++) {
    prod *= numbers[i];
}

It's possible you initialize prod to 0, which means no matter what numbers are in your array, prod will remain 0. Make sure you initialize it to 1 to get the correct result:

int prod = 1;
foreach (int value in numbers)
{
    prod *= value;
}

You could also use Linq's Aggregate extension method to do the same thing:

using System.Linq; // put with other using directives

int prod = numbers.Aggregate(1, (a, b) => a * b);

---

Update

The real problem (which I failed to notice before) is that your array isn't being fully populated if you break out of your loop early. So any array entries you didn't set are still initialized to 0. To fix this, use a List<int> instead of an int[]:

using System.Collections.Generic; // put with other using directives

List<int> numbers = new List<int>(SIZE); // Capacity == SIZE

...

for (int input = 0; input < SIZE; input++)
{
    ...
    if (numberInputed == ZERO)
    {
        break;
    }
    else
    {
        numbers.Add(numberInputed);
    }
}