Wordpress - Custom Taxonomy as checkbox or dropdown
As of WP 3.7 (https://core.trac.wordpress.org/ticket/14206) you can add this argument to register_taxonomy:
'meta_box_cb' => 'post_categories_meta_box'
to get the built-in checkbox category style metabox without having to make your taxonomy hierarchical.
Also you could instead provide your own callback function to create your own metabox (i.e. with a dropdown).
You probably did not set the 'hierarchical' argument to true in your register_taxonomy. This would mean that it defaults to false, which gives you a tag-like interface.
Add 'hierarchical' => true
to your register_taxonomy.