Sum all numbers in array function not returning the sum

Lots of basic issues with the code.

You need a separate variable to accumulate the result in. Your code is writing into the index variable of a for loop. This is wrong for a number of reasons.

You also return after the first iteration of the loop.

Assuming you want to use a for loop (which is not the least amount of code),

function sum(arr) {    
  var sum = 0;
  for (var index = 0; index < arr.length; index++) {
    sum += arr[index];
  }    
  return sum;
}

Use Array.reduce() for that:

function getSum(ary){
  return ary.reduce(function(sum, value) {
    return sum + value;
  }, 0);
}

console.log(getSum([0, 1, 2, 3]));

to illustrate where your code is wrong

function sum(arr) {
    var i = 0;

    for (var index = 0; index < arr.length; index++) {
        return index += arr[i]; // this will return from your function in the first iteration
    }
}

as the comment says, return will exit your function in the first iteration

also, you're adding to index, which is supposed to be the index into the array, you want to add to i, and then return i after the loop

so, the code should be

function sum(arr) {
    var i = 0;

    for (var index = 0; index < arr.length; index++) {
        i += arr[index];
    }

    return i;
}

As another answer pointed out, a probably better alternative is to use array reduce function - however the code in that answer is not the "best" usage of reduce

function getSum(ary){
    return ary.reduce(function(sum, value) {
        return sum + value;
    }, 0);
}

can actually be written

function getSum(ary){
    return ary.reduce(function(sum, value) {
        return sum + value;
    });
}

This uses one less iteration, because there is no "initial value", and the first iteration adds index 0 and 1 together

Sure, it's not going to make a performance difference, but why not use built-in functions properly :p

function Sum(arr) {

   var sum = 0;

   for (var index = 0; index < arr.length; index++) {
       sum += arr[index];
   }
   return index;

}

Sum([1, 2, 3]); //6

Return immediately exits a function. Your code will never sum values. What is 'i' in your code!?! And what index do!?

Here's how you get your function to work:

  function sum(arr) {
     // this is the variable we're going to add our numbers onto
     var acc = 0;

     for (var index = 0; index < arr.length; index++) {
        // don't return here, return is used to return from a function
        acc += arr[index];
     }
     // after adding all numbers, return the sum
     return acc
   }

   sum([1, 2, 3]); //6

But there are built in ways to do this, like Array.reduce() like Scott Marcus mentioned.