Max Chirkov

Advanced Text Widget is a text widget that allows you to execute raw PHP code and specify on which pages it should be displayed. It comes with 10 default visibility conditions. You can edit and/or add your own visibility conditions as well. Conditions support arguments which could be strings and/or arrays.
Features:
<ul>
<li>10 Default widget visibility conditions with over 20 application possibilities.</li>
<li>Add unlimited custom conditions.</li>
<li>“Advanced Text” widget with raw PHP support and shortcodes execution.</li>
</ul>
PRO Version:
<ul>
<li>Apply visibility conditions to ANY widget.</li>
<li>Add custom CSS IDs/Classes to ANY widget.</li>
<li>Import/Export your visibility conditions to re-use on other sites.</li>
</ul>
<a href="http://simplerealtytheme.com/plugins/atw-pro/" title="Advanced Text Widget PRO" rel="nofollow ugc">Check out PRO Version</a>
Credits:
<ul>
<li>Author: Max Chirkov</li>
<li>Author URI: <a href="http://SimpleRealtyTheme.com" title="Real Estate Themes for WordPress" rel="nofollow ugc">http://simplerealtytheme.com</a></li>
<li>Copyright: Released under GNU GENERAL PUBLIC LICENSE</li>
</ul>

Advanced Text Widget

2nd EDIT: The plugin has now been updated, so my original review stands.

1st EDIT: Even though this was a great plugin in its day, it hasn't been updated in over 2 years and was flagged as vulnerable to attack when I ran WPScan. I therefore can't recommend it for now.

Original review: Can't imagine building a WordPress site without this, it's normally the first plugin one I install. Makes adding custom content to sidebars on a per-page basis an absolute breeze. Very flexible, you can type PHP and shortcodes in the text area and it displays whatever you want. A must have for any WordPress site developer.

Essential plugin for all my sites

Text widget with raw PHP support and conditional visibility settings. Flexible conditional options with ability to edit and add custom conditions.

maennchen1.de

This plugin easily displays a weather widget with a destination of your choice. No PHP or Shortcode, just a widget. 
It caches the requests to the weather database in given intervals. 
You will need a free account at https://home.openweathermap.org/users/sign_up .
Font-Icons by Erik Flowers: https://erikflowers.github.io/weather-icons/

m1.MiniWeather

love the design

This plugin easily displays a weather widget (icon + temperature) with a destination of your choice.

Advanced Text Widget vs m1.MiniWeather