Stephanie Leary

This widget will list random posts from a chosen category. You can choose how many posts to display, and whether to show the excerpt or the full content in addition to the post title. You may also link the widget title to the category archive if you like.
<h3>Translations</h3>
Belorussian (be_BY) by <a href="http://fatcow.com" rel="nofollow ugc">FatCow</a>. 
Romanian (ro_RO) by Web Geek Science (<a href="http://webhostinggeeks.com/" rel="nofollow ugc">Web 
Hosting Geeks</a>)
If you would like to send me a translation, please write to me through <a href="http://sillybean.net/about/contact/" rel="nofollow ugc">my contact page</a>. Let me know which plugin you’ve translated and how you would like to be credited. I will write you back so you can attach the files in your reply.

Random Posts from Category

A widget that lists random posts from a chosen category.

wondermill

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.

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.

Random Posts from Category vs Random Posts with Thumbnails