Convert a javascript associative array into json object using stringify and vice versa

First of all, by making my_cars an array and stringifying it, you don't get what you expect.

var my_cars= new Array()
my_cars["cool"]="Mustang";
my_cars["family"]="Station Wagon";
my_cars["big"]="SUV";
alert(JSON.stringify(my_cars));

This alerts [].

What you want is to start with {}:

var my_cars= {};
my_cars["cool"]="Mustang";
my_cars["family"]="Station Wagon";
my_cars["big"]="SUV";
alert(JSON.stringify(my_cars));

This alerts

{"cool":"Mustang","family":"Station Wagon","big":"SUV"}

To get your object back from the string, use JSON.parse().

var s = JSON.stringify(my_cars);
var c = JSON.parse(s);
alert(c.cool);

This alerts "Mustang".

See http://jsfiddle.net/Y2De9/

Moving my comment into an answer so I can show you a code example.

These types of array are no-no's in javascript. You should ONLY use an object for non-numeric keys like this. Array indexes should be numbers. Javascript objects can use arbitrary values for keys (like in your example). Arrays happen to "appear" to work because Arrays themselves are objects, but you will not find normal Array methods will work on them. For example, look at this code example.

var my_cars= new Array()
my_cars["cool"]="Mustang";
my_cars["family"]="Station Wagon";
my_cars["big"]="SUV";
alert(my_cars.length);  // alerts 0

You have only added properties to the underlying object, not actually added elements to the Array. You should use an Object for this, not an Array. Javascript does not actually have an Associative Array. It has an Object who's properties can often be used like one would use an Associate Array in other languages. But, it's an Object, not an Array.