ng-repeat directive sort the data when using (key, value)

This is limitation of JavaScript not Angular.

From ECMAScript Third Edition:

4.3.3 An object is a member of the type Object. It is an unordered collection of properties each of which contains a primitive
value, object, or function. A function stored in a property of an
object is called a method.

From ECMAScript Language Specification

The […] order of enumerating the properties […]
is not specified.

Angular sorts object keys explicitly in order to provide at least some sort of persistent behavior.

Workaround is to iterate over extracted keys:

<div ng-repeat="key in keys(Dates)">
  {{key}} ==> {{Dates[key]}}
</div>

$scope.keys = function(obj){
  return obj? Object.keys(obj) : [];
}

$scope.Dates = {
  "Today":"30",
  "This Week":"42",
  "This Month": "Oct",
  "This Quarter" : "Bad",
  "This Year" : 2013
};