How to find the sum of an array of numbers

This'd be exactly the job for reduce.

If you're using ECMAScript 2015 (aka ECMAScript 6):

const sum = [1, 2, 3].reduce((partialSum, a) => partialSum + a, 0);
console.log(sum); // 6

For older JS:

const sum = [1, 2, 3].reduce(add, 0); // with initial value to avoid when the array is empty

function add(accumulator, a) {
  return accumulator + a;
}

console.log(sum); // 6

Isn't that pretty? :-)

Recommended (reduce with default value)

Array.prototype.reduce can be used to iterate through the array, adding the current element value to the sum of the previous element values.

console.log(
  [1, 2, 3, 4].reduce((a, b) => a + b, 0)
)
console.log(
  [].reduce((a, b) => a + b, 0)
)

Without default value

You get a TypeError

console.log(
  [].reduce((a, b) => a + b)
)

Prior to ES6's arrow functions

console.log(
  [1,2,3].reduce(function(acc, val) { return acc + val; }, 0)
)

console.log(
  [].reduce(function(acc, val) { return acc + val; }, 0)
)

Non-number inputs

If non-numbers are possible inputs, you may want to handle that?

console.log(
  ["hi", 1, 2, "frog"].reduce((a, b) => a + b)
)

let numOr0 = n => isNaN(n) ? 0 : n

console.log(
  ["hi", 1, 2, "frog"].reduce((a, b) => 
    numOr0(a) + numOr0(b))
)

Non-recommended dangerous eval use

We can use eval to execute a string representation of JavaScript code. Using the Array.prototype.join function to convert the array to a string, we change [1,2,3] into "1+2+3", which evaluates to 6.

console.log(
  eval([1,2,3].join('+'))
)

//This way is dangerous if the array is built
// from user input as it may be exploited eg: 

eval([1,"2;alert('Malicious code!')"].join('+'))

Of course displaying an alert isn't the worst thing that could happen. The only reason I have included this is as an answer Ortund's question as I do not think it was clarified.

Why not reduce? It's usually a bit counter intuitive, but using it to find a sum is pretty straightforward:

var a = [1,2,3];
var sum = a.reduce(function(a, b) { return a + b; }, 0);