Square brackets:

jsObj['key' + i] = 'example' + 1;

In JavaScript, all arrays are objects, but not all objects are arrays. The primary difference (and one that's pretty hard to mimic with straight JavaScript and plain objects) is that array instances maintain the length property so that it reflects one plus the numeric value of the property whose name is numeric and whose value, when converted to a number, is the largest of all such properties. That sounds really weird, but it just means that given an array instance, the properties with names like "0", "5", "207", and so on, are all treated specially in that their existence determines the value of length. And, on top of that, the value of length can be set to remove such properties. Setting the length of an array to 0 effectively removes all properties whose names look like whole numbers.

OK, so that's what makes an array special. All of that, however, has nothing at all to do with how the JavaScript [ ] operator works. That operator is an object property access mechanism which works on any object. It's important to note in that regard that numeric array property names are not special as far as simple property access goes. They're just strings that happen to look like numbers, but JavaScript object property names can be any sort of string you like.

Thus, the way the [ ] operator works in a for loop iterating through an array:

for (var i = 0; i < myArray.length; ++i) {
  var value = myArray[i]; // property access
  // ...
}

is really no different from the way [ ] works when accessing a property whose name is some computed string:

var value = jsObj["key" + i];

The [ ] operator there is doing precisely the same thing in both instances. The fact that in one case the object involved happens to be an array is unimportant, in other words.

When setting property values using [ ], the story is the same except for the special behavior around maintaining the length property. If you set a property with a numeric key on an array instance:

myArray[200] = 5;

then (assuming that "200" is the biggest numeric property name) the length property will be updated to 201 as a side-effect of the property assignment. If the same thing is done to a plain object, however:

myObj[200] = 5;

there's no such side-effect. The property called "200" of both the array and the object will be set to the value 5 in otherwise the exact same way.

One might think that because that length behavior is kind-of handy, you might as well make all objects instances of the Array constructor instead of plain objects. There's nothing directly wrong about that (though it can be confusing, especially for people familiar with some other languages, for some properties to be included in the length but not others). However, if you're working with JSON serialization (a fairly common thing), understand that array instances are serialized to JSON in a way that only involves the numerically-named properties. Other properties added to the array will never appear in the serialized JSON form. So for example:

var obj = [];
obj[0] = "hello world";
obj["something"] = 5000;

var objJSON = JSON.stringify(obj);

the value of "objJSON" will be a string containing just ["hello world"]; the "something" property will be lost.

ES2015:

If you're able to use ES6 JavaScript features, you can use Computed Property Names to handle this very easily:

var key = 'DYNAMIC_KEY',
    obj = {
        [key]: 'ES6!'
    };

console.log(obj);
// > { 'DYNAMIC_KEY': 'ES6!' }

In the new ES2015 standard for JavaScript (formerly called ES6), objects can be created with computed keys: Object Initializer spec.

The syntax is:

var obj = {
  [myKey]: value,
}

If applied to the OP's scenario, it would turn into:

stuff = function (thing, callback) {
  var inputs  = $('div.quantity > input').map(function(){
    return {
      [this.attr('name')]: this.attr('value'),
    };
  }) 

  callback(null, inputs);
}

Note: A transpiler is still required for browser compatiblity.

Using Babel or Google's traceur, it is possible to use this syntax today.

In earlier JavaScript specifications (ES5 and below), the key in an object literal is always interpreted literally, as a string.

To use a "dynamic" key, you have to use bracket notation:

var obj = {};
obj[myKey] = value;

In your case:

stuff = function (thing, callback) {
  var inputs  = $('div.quantity > input').map(function(){
    var key   = this.attr('name')
     ,  value = this.attr('value')
     ,  ret   = {};

     ret[key] = value;
     return ret;
  }) 

  callback(null, inputs);
}