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 }

Update

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 }

Array.prototype.reduce reduces an array to a single value by somewhat merging the previous value with the current. The chain is initialized by an empty object {}. On every iteration a new key of myObject is added with twice the key as the value.

Update

With new ES6 features, there is a more elegant way to express objectMap.

const objectMap = (obj, fn) =>
  Object.fromEntries(
    Object.entries(obj).map(
      ([k, v], i) => [k, fn(v, k, i)]
    )
  )

const myObject = { a: 1, b: 2, c: 3 }

console.log(objectMap(myObject, v => 2 * v))