Theme Tester by Donncha is possibly one of the simplest but most useful plugins I personally use on a day to day basis, it essentially allows you to set two themes, one for visitors of websites and the other for logged in administrators.
The plugin is so simple to use that it only requires one option, either the theme tester is set to active so that a private theme is in use de active meaning all users can see the same theme.
I’ll mainly use this plugin to work on theme modifications or upgrades which need testing before putting live, this tool allows me try test drive themes without taking a website down or causing users any inconvenience as anyone visiting the site will just be show the current theme.