Ruven

This plugin registers a custom post type for galleries and a taxonomy for categories.
Selected themes by Ruven provide templates to display galleries. 
In other themes you most likely have to add them by yourself.

Ruven Themes: Gallery

RT Gallery enables a "Gallery" post type and "Category" taxonomy.

George Pattichis

Simple CPT is a free WordPress plugin that lets you create custom post types and custom taxonomies (eg: categories, tags, etc.) directly from your admin dashboard without writing a single line code.
No more editing files manually. With Simple CPT you can create a new Custom Post Type in less than 1 minute.
This plugin is written using only native functions, included in WordPress core, so it does not in any way reduce the performance of your website and will not cause any compatibility problems. Simple CPT is completely free, it will save you time and it is compatible with almost all themes and plugins out there.
In just a few minutes you can adapt your WordPress site to any type of project in a professional and extremely efficient way, e.g. ecommerce, hotel, restaurant, events, portfolio, community websites etc.

Simple CPT

Simple CPT provides an easy to use interface for registering and managing custom post types and custom taxonomies.

Ruven Themes: Gallery vs Simple CPT