Pete

Note: Obsolete since WordPress 4.4
<a href="https://core.trac.wordpress.org/ticket/32230" rel="nofollow ugc">This feature has been added into the core of WordPress 4.4</a>. You can now export your attachments by going to Tools->Export and select ‘Media’ as the export type.
Original Description
WP Attachment Export allows you to export your media library into a WordPress eXtended RSS or WXR file. You can then use the Tools->Import function in another WordPress installation to import the media library.
<h4>Issues / Bug reporting</h4>
Found a bug? Please use the issue tracker at <a href="https://github.com/thehelvetian/wp-attachment-export/issues" rel="nofollow ugc">https://github.com/thehelvetian/wp-attachment-export/issues</a>
<h3>Usage</h3>
User <a href="https://wordpress.org/support/profile/philho" rel="ugc">PhiLho</a> has put together a good summary on how to use the plugin at <a href="https://wordpress.org/support/topic/good-but-could-use-more-explanations" rel="ugc">https://wordpress.org/support/topic/good-but-could-use-more-explanations</a>. Thanks PhiLho!

WP Attachment Export

works perfectly.

Exports only posts of type 'attachment', i.e. your media library

Marco Milesi

WP Attachments enhances the download experience and file management in WordPress. It automatically displays attachments in your posts and pages, so you don’t need to manually insert download links. 
Easily attach, unattach, or reattach files directly from the media library.
Key Features: 
– 🤖 Automatically displays attachments after post content 
– ℹ️ Backend metabox for managing attachments 
– 🔃 Quick Attach, Unattach, and Reattach actions in the Media Library 
– 🔢 Download counter with anti-spam and logged-in user filtering 
– 🧑‍💻 Developer hooks and filters for customization 
– 🛍️ WooCommerce compatible 
– 🎨 Five icon packs to choose from 
– 📜 Supports posts, pages, and custom post types 
– 🎢 Customizable themes (title, date, size, caption, and more)
<a href="https://www.youtube.com/watch?v=J7gf0hxl_z8" rel="nofollow ugc">Video Overview</a>
<h3>Contributions</h3>
<ul>
<li>Part of <a href="http://www.wpgov.it" rel="nofollow ugc">WPGov.it</a>, providing open source solutions for Italian Public Government websites.</li>
<li>Thanks to the Italian community <a href="http://www.porteapertesulweb.it" rel="nofollow ugc">Porte Aperte sul Web</a> for beta testing and ideas.</li>
<li>Metabox based on <a href="https://wordpress.org/plugins/ij-post-attachments/" rel="ugc">IJ Post Attachments</a></li>
<li>Some icons by <a href="http://p.yusukekamiyamane.com/" rel="nofollow ugc">Yusuke Kamiyamane</a>.</li>
</ul>

WP Attachments

Nice and useful plugin. The only downside is that it lacks a setting to show image thumbnails instead of a generic image icon in the edit metabox.

Show thumbnails instead of icons in metabox

A powerful solution to manage and display your WordPress media attachments in posts and pages.

WP Attachment Export vs WP Attachments