You didn't put return before this.traverse(data[i].children, pk);.
EDIT:
var Tree = {
    data: {
        0: {
            pk: 1,
        },
        1: {
            pk: 2,
        },
        2: {
            pk: 3,
            children: {
                0: {
                    pk: 11,
                },
                1: {
                    pk: 22,
                },
                2: {
                    pk: 33,
                },
            },
        },
    },
    traverse: function(data, pk) {
        for (var i in data) {
            // console.log(data[i]);
            if(data[i].pk && data[i].pk == pk)
                return data[i];
            if (typeof(data[i].children) == 'object') {
                var retVal = this.traverse(data[i].children, pk);
                if (typeof retVal!='undefined') {//here was the logical problem,there might be more than one
                                                 //object, we can't return the result of traversing first one.
                                                 //So we will check, if no return, we go on searching
                    return retVal;
                }
            }
        };
    },
};
alert(Tree.traverse(Tree.data, 1).pk);
alert(Tree.traverse(Tree.data, 22).pk);
check live here: http://jsfiddle.net/rq4LK/