lupka

This plugin allows you to create a widget that will display the title/date/excerpt from random posts in a specified(or open-ended) date range. It can also be used outside of a widget to create custom loops of random posts within a date range. The following can be specified:
<ul>
<li>Number of posts to display</li>
<li>Whether or not to show dates</li>
<li>Whether or not to show excerpts</li>
<li>Excerpt length (number of words)</li>
<li>Start date and End date of posts to randomize</li>
<li>Whether or not to always use current date as end. (Allows you to include new posts without editing settings every day)</li>
<li>Option to use relative time instead (To chose from random posts from last week, year, etc.)</li>
<li>Category to choose posts from. (Example: Random posts from sports category in the past week. This is the original reason I needed a plugin like this. Comes in handy for the newspaper site I run.)</li>
</ul>
Please contact me if you run into any issues, either via email (lupka31@gmail.com) or Twitter (http://twitter.com/lupka) 
For latest FAQs/info visit: http://alexchalupka.com/projects/wordpress/random-posts-widget/

Random Posts Within Date Range Widget

Widget that displays the title(w/ link), date(optional), and excerpt(optional) of random posts within a selected date range.

Scribit

With Random plugin you can insert into your WordPress website one or more random contents coming from your posts. 
The source contents can be pages, posts or custom post types. 
You can display information in many different ways: 
* A list of post titles 
* One or more full contents or excerpts 
* Raw URLs to posts permalink

Random

This plugin give to your website the possibility to get random content for specific posts types. You can use to give to your visitors random posts, or random woocommerce products for your clients.
Very useful in my opinion.

Wikipedia style!

Random, a great plugin designed to insert random contents, posts and other types, into your website. Enjoy its shortcodes!

Random Posts Within Date Range Widget vs Random