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

mahavirnahata

Sticky Recent Random Posts is awesome Plugin that let users to show sticky bar at bottom, that sticky bar will contain random Title of Recent Posts(Including Custom Post Types). This plugin will help to engage more users and help to reduce Bounce rate.
This plugin comes with a Setting Page through which user can customize Appearance and other settings. This option page is located under Settings Menu.
What this plugin do : 
This plugin will show sticky bar at bottom part of page, that sticky bar will contain <code>Title</code> of recent post, that recent post is randomly selected. You also have option to choose whether to open that link in current window or new window. You can customize colors, Opacity, number of last recent post to shuffle from and other settings.
You will love this plugin for sure, as it will decrease Bounce Rate of your blog and will engage more visitors by displaying random post. Due to its sticky behaviour it will capture attention of user easily.
<a href="http://offersday.in/sticky-recent-random-posts/" title="Plugin Demo" rel="nofollow ugc">You can see Live working demo here.</a>
Hoping that you will like this plugin. Don`t forget to rate this plugin or write your valuable opinion that will guide us to make it more useful in future release.

Sticky Recent Random Posts

Sticky Recent Random Posts Plugin lets user to add sticky bar at bottom.

Random One Cat Widget vs Sticky Recent Random Posts