There are times when you’d like to have a certain type of post appear in a widget for use in your sidebar or (in some themes) your header or footer.
I used this to display a random senryu on each page, but it will work equally well for any group of reasonably small posts.
There is the option to include the title of the post, the title of the widget, both titles, or neither.
If you want you can add a bunch of widgets, each showing up to five random posts from a different category.

Random One Cat Widget

This Widget shows up to five random posts from a given category

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 One Cat Widget vs Random