dev.Fishy

EN:
Adds a simple widget to the sidebar that displays a random posts.
RU:
Добавляет простой виджет в боковую панель сайта, который отображает случайные посты.

RandPost widget

Xoda

Random Post Box is a plugin that lets you place a box anywhere on your blog, with template tag or shortcode, and 
load random posts with an interval and fade effect. It uses jQuery (Ajax) which means that the content is loaded without 
loading the rest of the page. The timings can be set in the admin options-panel.
The template tag is <code><?php random_post_box(); ?></code>. You can also use the shortcode <code>[random-post-box]</code> in a page or post.
<h4>Features</h4>
<ul>
<li>Insert placeholder with template tag</li>
<li>Insert placeholder with shortcode</li>
<li>Set time for displaying the post</li>
<li>Set times for fade in and fade out affect</li>
<li>Exclude or include posts by category</li>
<li>Exclude posts by age (in days)</li>
<li>Use title only</li>
<li>Use post excerpt or bodycontent</li>
<li>Strip tags from body</li>
<li>Show/hide post metadata</li>
</ul>

Random Post Box

The Random Post Box plugin places a box anywhere on the blog, where it loads random posts one-after-the-other.

RandPost widget vs Random Post Box