How can I extend a UI component JavaScript in Magento 2?

This can be accomplished using a requirejs "mixin".

First create Your_Module/view/base/requirejs-config.js with this code:

var config = {
    'config': {
        'mixins': {
            'Magento_Ui/js/form/form': {
                'Your_Module/form-hook': true
            }
        }
    }
};

Now make the file Your_Module/view/base/web/form-hook.js :

define([], function () {
    'use strict';

    return function (Form) {
        return Form.extend({
            initialize: function () {
                this._super();
                console.log('Hello from the mixin!');
            }
        });
    }
});

This example extends the initialize method of the form component.

You can read more about "mixins" here: http://alanstorm.com/the-curious-case-of-magento-2-mixins/