looping through an object (tree) recursively

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... 
    }
}