So .map itself only offers one value you care about... That said, there are a few ways of tackling this:

// instantiation
const myMap = new Map([
  [ "A", 1 ],
  [ "B", 2 ]
]);

// what's built into Map for you
myMap.forEach( (val, key) => console.log(key, val) ); // "A 1", "B 2"

// what Array can do for you
Array.from( myMap ).map(([key, value]) => ({ key, value })); // [{key:"A", value: 1}, ... ]

// less awesome iteration
let entries = myMap.entries( );
for (let entry of entries) {
  console.log(entry);
}

Note, I'm using a lot of new stuff in that second example... ...Array.from takes any iterable (any time you'd use [].slice.call( ), plus Sets and Maps) and turns it into an array... ...Maps, when coerced into an array, turn into an array of arrays, where el[0] === key && el[1] === value; (basically, in the same format that I prefilled my example Map with, above).

I'm using destructuring of the array in the argument position of the lambda, to assign those array spots to values, before returning an object for each el.

If you're using Babel, in production, you're going to need to use Babel's browser polyfill (which includes "core-js" and Facebook's "regenerator").
I'm quite certain it contains Array.from.

There is no native map to the Object object, but how about this:

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

Object.keys(myObject).forEach(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))