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// There is no native map to the Object object, but how about this:
var myObject = { 'a': 1, 'b': 2, 'c': 3 };

Object.keys(myObject).map(function(key, index) {
  myObject[key] *= 2;
});

console.log(myObject);
// => { 'a': 2, 'b': 4, 'c': 6 }

// But you could easily iterate over an object using for ... in:

var myObject = { 'a': 1, 'b': 2, 'c': 3 };

for (var key in myObject) {
  if (myObject.hasOwnProperty(key)) {
    myObject[key] *= 2;
  }
}

console.log(myObject);
// { 'a': 2, 'b': 4, 'c': 6 }

// A lot of people are mentioning that the previous methods do not return a new object, but rather operate on the object itself. For that matter I wanted to add another solution that returns a new object and leaves the original object as it is:
var myObject = { 'a': 1, 'b': 2, 'c': 3 };

// returns a new object with the values at each key mapped using mapFn(value)
function objectMap(object, mapFn) {
  return Object.keys(object).reduce(function(result, key) {
    result[key] = mapFn(object[key])
    return result
  }, {})
}

var newObject = objectMap(myObject, function(value) {
  return value * 2
})

console.log(newObject);
// => { 'a': 2, 'b': 4, 'c': 6 }

console.log(myObject);
// => { 'a': 1, 'b': 2, 'c': 3 }

// How about a one liner with immediate variable assignment in plain JS (ES6 / ES2015) ?
// Making use of spread operator and computed key name syntax:
let newObj = Object.assign({}, ...Object.keys(obj).map(k => ({[k]: obj[k] * obj[k]})));

// Another version using reduce:
let newObj = Object.keys(obj).reduce((p, c) => ({...p, [c]: obj[c] * obj[c]}), {});

// First example as a function:
const oMap = (o, f) => Object.assign({}, ...Object.keys(o).map(k => ({ [k]: f(o[k]) })));
// To square each value you can call it like this:
let mappedObj = oMap(myObj, (x) => x * x);

// If you want to map a nested object recursively in a functional style, it can be done like this:
const sqrObjRecursive = obj =>
  Object.keys(obj).reduce(
    (newObj, key) =>
      obj[key] && typeof obj[key] === "object"
        ? { ...newObj, [key]: sqrObjRecursive(obj[key]) } // recurse.
        : { ...newObj, [key]: obj[key] * obj[key] }, // square val.
    {}
  );
  
// Or more imperatively, like this:
const sqrObjRecursive = obj => {
  Object.keys(obj).forEach(key => {
    if (typeof obj[key] === "object") obj[key] = sqrObjRecursive(obj[key]);
    else obj[key] = obj[key] * obj[key];
  });
  return obj;
};

// Since ES7 / ES2016 you can use Object.entries() instead of Object.keys() e.g. like this:
let newObj = Object.assign(...Object.entries(obj).map(([k, v]) => ({[k]: v * v})));

// ES2019 might introduce Object.fromEntries(), which simplifies this even more:
let newObj = Object.fromEntries(Object.entries(([key, val]) => [k, v * v]));

// Inherited properties and the prototype chain:
// In some rare situation you may need to map a class-like object which holds properties of an inherited object on its prototype-chain. In such cases Object.keys() won't work, because Object.keys() does not enumerate inherited properties. If you need to map inherited properties, you should use for (key in myObj) {...}.

// Here is an example of an object which inherits the properties of another object and how Object.keys() doesn't work in such scenario.

const obj1 = { 'a': 1, 'b': 2, 'c': 3}
const obj2 = Object.create(obj1);  // One of multiple ways to inherit an object in JS.

// Here you see how the properties of obj1 sit on the 'prototype' of obj2
console.log(obj2)  // Prints: obj2.__proto__ = { 'a': 1, 'b': 2, 'c': 3}

console.log(Object.keys(obj2));  // Prints: an empty Array.

for (key in obj2) {
  console.log(key);              // Prints: 'a', 'b', 'c'
}

// However, please do me a favor and avoid inheritance. :-)

// No native methods, but lodash#mapValues will do the job brilliantly

_.mapValues({ 'a': 1, 'b': 2, 'c': 3} , function(num) { return num * 3; });
// → { 'a': 3, 'b': 6, 'c': 9 }