map function for objects (instead of arrays)

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]})));

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Another version using reduce:

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

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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);

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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.
    {}
  );       

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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;
};

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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 introduced Object.fromEntries(), which simplifies this even more:

let newObj = Object.fromEntries(Object.entries(obj).map(([k, v]) => [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'
}

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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 }

It's pretty easy to write one:

Object.map = function(o, f, ctx) {
    ctx = ctx || this;
    var result = {};
    Object.keys(o).forEach(function(k) {
        result[k] = f.call(ctx, o[k], k, o); 
    });
    return result;
}

with example code:

> o = { a: 1, b: 2, c: 3 };
> r = Object.map(o, function(v, k, o) {
     return v * v;
  });
> r
{ a : 1, b: 4, c: 9 }

NB: this version also allows you to (optionally) set the this context for the callback, just like the Array method.

EDIT - changed to remove use of Object.prototype, to ensure that it doesn't clash with any existing property named map on the object.

You could use Object.keys and then forEach over the returned array of keys:

var myObject = { 'a': 1, 'b': 2, 'c': 3 },
    newObject = {};
Object.keys(myObject).forEach(function (key) {
    var value = myObject[key];
    newObject[key] = value * value;
});

Or in a more modular fashion:

function map(obj, callback) {
    var result = {};
    Object.keys(obj).forEach(function (key) {
        result[key] = callback.call(obj, obj[key], key, obj);
    });
    return result;
}

newObject = map(myObject, function(x) { return x * x; });

Note that Object.keys returns an array containing only the object's own enumerable properties, thus it behaves like a for..in loop with a hasOwnProperty check.

This is straight bs, and everyone in the JS community knows it. There should be this functionality:

const obj1 = {a:4, b:7};
const obj2 = Object.map(obj1, (k,v) => v + 5);

console.log(obj1); // {a:4, b:7}
console.log(obj2); // {a:9, b:12}

here is the naïve implementation:

Object.map = function(obj, fn, ctx){

    const ret = {};

    for(let k of Object.keys(obj)){
        ret[k] = fn.call(ctx || null, k, obj[k]);
    });

    return ret;
};

it is super annoying to have to implement this yourself all the time ;)

If you want something a little more sophisticated, that doesn't interfere with the Object class, try this:

let map = function (obj, fn, ctx) {
  return Object.keys(obj).reduce((a, b) => {
    a[b] = fn.call(ctx || null, b, obj[b]);
    return a;
  }, {});
};


const x = map({a: 2, b: 4}, (k,v) => {
    return v*2;
});

but it is safe to add this map function to Object, just don't add to Object.prototype.

Object.map = ... // fairly safe
Object.prototype.map ... // not ok