Josh Pollock

Use this plugin to create a demo site for your themes, or use it to allow users to customize the presentation of your site.
The JP Theme Bar Plugin adds a theme switching bar to the bottom of your site, perfect for theme preview sites. The settings page for the plugin lets the end user choose which themes to add, as well as set the colors for the theme bar. You can see it in action on this site.
New in version 0.0.3 -> Themes will update theme mods when changing themes allowing for individual theme settings to be previewed properly.
This plugin is based on the <a href="http://iainjmccallum.com/wordpress/live-demo-theme-bar/" rel="nofollow ugc">IJM Theme Switcher Bar v2.0</a> by <a href="http://www.iainjmccallum.com/" rel="nofollow ugc">Iain J McCallum</a>
IMPORTANT- The plugin <a href="https://wordpress.org/plugins/theme-test-drive/" rel="ugc">Theme Test Drive</a> by <a href="http://www.prelovac.com/vladimir/" rel="nofollow ugc">Vladimir Prelovac</a> must be installed and activated in order for the theme switching to work.

JP Theme Switcher Bar

Adds a theme switcher/ theme demo bar to the bottom of your site to allow users to switch the theme they see on your site.

xhtmlweaver

In short, this plugin allows you to modify/switch the current theme with live site on the fly without messing up with your current visitors. 
This plugin is perfect for WordPress theme developers, freelancers as it allows you to edit the live theme without interfering the current visitors. 
It offers following features:
<ul>
<li>Ability to duplicate any current themes to the new theme for editing purpose.</li>
<li>Selectively enabling the theme switcher on the frontend by enabling extra settings in the backend. (By role or by IP Addresses)</li>
<li>Provides an Ajax theme switcher on the right top which selectively allows the visitor (by role or IP Addresses) to switch the theme.</li>
<li>A transparent banner on the top to display current theme.</li>
<li>Full Support is available at http://www.xhtmlweaver.com or wp-support@xhtmlweaver.com</li>
</ul>

Parallels Themes Switcher

This plugin allows you to modify/switch the current theme on the live site without interfering the current visitors.

JP Theme Switcher Bar vs Parallels Themes Switcher