Drupal - How do I programmatically generate an entity form?

You can use the entity form builder service. I was able to load the user form this way (with $entity being the current user):

$entity = User::load($uid);
$user_form = \Drupal::service('entity.form_builder')->getForm($entity, 'default');

If you want to get the user register form (which is basically an entity form without a saved entity), you can just use the create method on your entity class before passing it to the form:

$entity = User::create();
$user_form = \Drupal::service('entity.form_builder')->getForm($entity, 'default');

Entity forms don't work without an entity. If you want an empty form then use a newly created entity instance. You can use this example from the node entity:

/**
 * Provides the node submission form.
 *
 * @param \Drupal\node\NodeTypeInterface $node_type
 *   The node type entity for the node.
 *
 * @return array
 *   A node submission form.
 */
public function add(NodeTypeInterface $node_type) {
  $node = $this->entityManager()->getStorage('node')->create(array(
    'type' => $node_type->id(),
  ));

  $form = $this->entityFormBuilder()->getForm($node);

  return $form;
}

The entity form builder is injected in the controller base class. So usually you use a controller to build entity forms.

When creating a node you need to define a bundle (content type), for which the entity form will be built. If your entity has no bundles you can use an empty array.

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Comments

Comments need more work, because they are attached to an entity field.

Example how to build a form for the comment field of a node:

$comment = $this->entityTypeManager()->getStorage('comment')->create([
  'entity_type' => 'node',
  'entity_id' => $node->id(),
  'field_name' => 'comment',
]);
$build = $this->entityFormBuilder()->getForm($comment);

Or the same outside of a controller without injected services:

$comment = \Drupal::entityTypeManager()->getStorage('comment')->create([
  'entity_type' => 'node',
  'entity_id' => $node->id(),
  'field_name' => 'comment',
]);
$build = \Drupal::service('entity.form_builder')->getForm($comment);

Just to clarify, the below code does work for me in Drupal 8.2.x:

$form = \Drupal::formBuilder()->getForm(Drupal\user\Form\UserLoginForm::class);