I made a FIDDLE for you. I am storing a stack string and then output it, if the property is of primitive type:

function iterate(obj, stack) {
        for (var property in obj) {
            if (obj.hasOwnProperty(property)) {
                if (typeof obj[property] == "object") {
                    iterate(obj[property], stack + '.' + property);
                } else {
                    console.log(property + "   " + obj[property]);
                    $('#output').append($("<div/>").text(stack + '.' + property))
                }
            }
        }
    }

iterate(object, '')

Update: 17/01/2019

There used to be a different implementation, but it didn't work. See this answer for a prettier solution

You're looking for the for...in loop:

for (var key in foo)
{
    if (key == "child")
        // do something...
} 

Be aware that for...in loops will iterate over any enumerable properties, including those that are added to the prototype of an object. To avoid acting on these properties, you can use the hasOwnProperty method to check to see if the property belongs only to that object:

for (var key in foo)
{
    if (!foo.hasOwnProperty(key))
        continue;       // skip this property
    if (key == "child")
        // do something...
}

Performing the loop recursively can be as simple as writing a recursive function:

// This function handles arrays and objects
function eachRecursive(obj)
{
    for (var k in obj)
    {
        if (typeof obj[k] == "object" && obj[k] !== null)
            eachRecursive(obj[k]);
        else
            // do something... 
    }
}

First: You neither need nor want eval for any of this. Start with $ (the object) and then use obj[key] when you are looking into one of its properties. Recurse when that property is a non-function object.

The reason you're not seeing all of the properties is that for-in loops only loop through enumerable properties, and many of jQuery's properties are not enumerable. You can use getOwnPropertyNames to get the names of all string-keyed properties of an object, even non-enumerable ones. And you can use getPrototypeOf to get that object's prototype so you can enumerate its properties (which for-in does).

So:

function showData(name, obj)
{
    while (obj && obj != Object.prototype)
    {
        // Get all of the object's property names, even non-enumerable ones
        var keys = Object.getOwnPropertyNames(obj);
        keys.forEach(function(key)
        {
            // We should restrict this check to function objects; left
            // as an exercise for the reader...
            if (key !== "caller" &&
                key !== "callee" &&
                key !== "arguments"
                )
            {
                var value = obj[key];
                var type = typeof value;
                debugWriteLine('object = ' + name + ' | property = ' + key + ' | type = ' + type + ' | value = ' + value); 

                if (type === 'object')
                {
                    return showData(name + "." + key, value);
                }
            }
        });

        // Get the object's prototype
        obj = Object.getPrototypeOf(obj);
    }
}

Live Example:

var debugWriteLine = console.log.bind(console);
function showData(name, obj)
{
    while (obj && obj != Object.prototype)
    {
        // Get all of the object's property names, even non-enumerable ones
        var keys = Object.getOwnPropertyNames(obj);
        keys.forEach(function(key)
        {
            // We should restrict this check to function objects; left
            // as an exercise for the reader...
            if (key !== "caller" &&
                key !== "callee" &&
                key !== "arguments"
                )
            {
                var value = obj[key];
                var type = typeof value;
                debugWriteLine('object = ' + name + ' | property = ' + key + ' | type = ' + type + ' | value = ' + value); 

                if (type === 'object')
                {
                    return showData(name + "." + key, value);
                }
            }
        });

        // Get the object's prototype
        obj = Object.getPrototypeOf(obj);
    }
}

showData('$', $);

.as-console-wrapper {
  max-height: 100% !important;
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>