DuncanMarshall

This widget displays the current star sign, your zodiac sign, or a calculator to let users pick their’s.
<ul>
<li>Clean, simple, and responsive design fits well with any theme</li>
<li>Keeps users coming back to your site.</li>
<li>Works equally well on desktop or mobile.</li>
</ul>
The widget renders html anchors to static alternatives for users with NoScript, but requires you to enable this feature.

Show Star Sign Widget

A sidebar widget to display a star sign - yours, or the current sign.

NipponMonkey

This plugin automatically logs a user out after a certain period of time of inactivity. 
It creates new meta data for each WP user and checks that the user hasn’t been inactive for too long. 
If the user has been inactive for too long, then the user is automatically logged out and redirected to a URL of your choice. 
It tracks the users activity in both the main site and admin area.
You can set the maximum inactivity time and redirect URL by changing the defined constants in the plugin’s PHP page – no admin menus are available yet see FAQs.
It’s only a single PHP page, so it’s easy to alter to work however you’d like it to work.
It works with BuddyPress too.
Let me know if you find a better way of doing this, and I’ll update the plugin.
<h3>Installation Bug</h3>
[FIXED!] Currently, when you activate the plugin, you are automatically logged out!

Inactivity Auto Sign Out Plugin

This plugin automatically logs out the user after a period of inactivity. The time period can be configured and it works with BuddyPress.

Show Star Sign Widget vs Inactivity Auto Sign Out Plugin