Index signatures

It is possible to denote obj as any, but that defeats the whole purpose of using typescript. obj = {} implies obj is an Object. Marking it as any makes no sense. To accomplish the desired consistency an interface could be defined as follows, using an index signature

interface LooseObject {
    [key: string]: any
}

var obj: LooseObject = {};

OR to make it compact:

var obj: {[k: string]: any} = {};

LooseObject can accept fields with any string as key and any type as value.

obj.prop = "value";
obj.prop2 = 88;

The real elegance of this solution is that you can include typesafe fields in the interface.

interface MyType {
    typesafeProp1?: number,
    requiredProp1: string,
    [key: string]: any
}

var obj: MyType ;
obj = { requiredProp1: "foo"}; // valid
obj = {} // error. 'requiredProp1' is missing
obj.typesafeProp1 = "bar" // error. typesafeProp1 should be a number

obj.prop = "value";
obj.prop2 = 88;

Record<Keys,Type> utility type

Update (August 2020): @transang brought up the Record<Keys,Type> utility type in comments

Record<Keys,Type> is a Utility type in typescript. It is a much cleaner alternative for key-value pairs where property-names are not known. It's worth noting that Record<Keys,Type> is a named alias to {[k: Keys]: Type} where Keys and Type are generics. IMO, this makes it worth mentioning here

For comparison,

var obj: {[k: string]: any} = {};

becomes

var obj: Record<string,any> = {}

MyType can now be defined by extending Record type

interface MyType extends Record<string,any> {
    typesafeProp1?: number,
    requiredProp1: string,
}

While this answers the Original question, the answer here by @GreeneCreations might give another perspective on how to approach the problem.

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);
}