wondermill

<p>If you want to graphically display a random list of your posts with their featured image in the side bar, then this is the plugin for you. This plugin allows you to set the category IDs (or all categories) you want to pull the random posts from, the number of random posts to display, the maximum width and height of the featured image thumbnail, the widget title, and the colors of the surrounding box.</p>


Random Posts with Thumbnails

Puts a list of clickable random posts with their featured image in your sidebar as a widget, this list is customizable.

pantsonhead

<p>RandomText is a handy WordPress plugin that allows you to save, edit and delete categorized text, and inject random/rotated text by category into the sidebar (via widget) or page body (via template tags). The sidebar widget allows you to set an optional Title, and text header and footer. You could say RandomText picks up where the Text widget left off. Whether you want to display random/rotated trivia, quotes, helpful hints, featured articles, or snippets of html, you can do it all easily with RandomText.</p>


Random Text

Store and display random/rotated text by category in sidebar widget or templates.

Random Posts with Thumbnails vs Random Text