Create a renderable array for checkbox

Assuming that your render array is part of a form (outside of which a checkbox doesn't make a whole lot of sense), you would do it like this:

$form['checkbox'] = array(
  '#type' => 'checkbox',
  '#title' => 'Title',
  '#default_value' => 1, // Checked by default
);

Have a look at the checkbox type documentation for all of the available properties.

EDIT

Just to add that render($form['checkbox']); also works perfectly outside of the form context using the above code; the correct checkbox element is rendered, but without the "name" and "id" attributes.