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.

Copyconsole.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

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

Prior to ES6's arrow functions

Copyconsole.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?

Copyconsole.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))
)

Speed Optimized

The reduce way is nice as it is easy to write and generally simple to understand, but if you are looking for speed (which is usually not a concern), use a simple for loop.

Copyconst numbers = [1, 2, 3, 4];
let sum = 0;
for (let i = 0; i < numbers.length; i++) {
  sum += numbers[i];
}
console.log(sum);

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.

Copyconsole.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.