Paul Gregory

Adds three widgets – “Text/List”, “Text/List (If Logged In)” and “Text/List (Not Logged In)”. These can be used much like the normal Text widget, except two of them only display if the condition is met.
Potential Uses: 
* Add a link to a Register page, along with some text promoting registration (for example on a site with the bbPress plugin) 
* Display adverts to users who are not logged in 
* Display useful links to users who are logged in. 
* Display a nice list to everyone.
Because the widgets are separate, you can have the logged-in widget in a different place to a logged-out widget. You don’t even have to have pairs of widgets.
Unlike the normal Text widget which just has a toggle for paragraph on/off, this widget has four display options:
<ul>
<li>No formatting</li>
<li>Add paragraphs</li>
<li>Bullet list (ul)</li>
<li>Numbered list (ol)</li>
</ul>
The list options are useful if you are adding a number of links – simply add each one on a new line and they’ll be turned into a bullet. Please note that this plugin adds no CSS. Often themes style the lists within a widget to make menus look nice, so your theme may (for example) prevent numbers from showing. See FAQ.
You may find that the Text/List widget is useful even without the logged-in / logged-out conditional.

Logged In Conditional Text Widget

Adds text/list widgets - one only shows if user is logged in, and the other only shows if a user is not logged in. A third shows regardless.

geomagas

This plugin provides an [if] shortcode to conditionally render content. The syntax is the following:
<pre><code>[if condition1 condition2=false condition3]{content}[/if]
</code></pre>
Conditions are passed as attribute names. Multiple conditions evaluate to the result of ORing all of them. In other words, if at least one condition evaluates to the desired boolean result, {content} is rendered, otherwise it is discarded. 
Attribute values determine if we want the condition to be true or false. A value of <code>'0'</code>, <code>'false'</code>, <code>''</code> (the empty string), <code>'null'</code> or <code>'no'</code> means we expect the condition to be false. Anything else, including the absense of a value, is interpreted as true.
For example, suppose that we want to include a sentence in a post, but only for anonymous visitors:
<pre><code>[if is_user_logged_in=no]The Sentence.[/if]
</code></pre>
It also provides an [else] shortcode and an [eitherway] one for use inside [if] blocks. [else] will render its content if the condition evaluates to false, and [eitherway] will render its content regardless of the evaluation result. 
When used outside an [if] block, these shortcodes behave as if the whole content is surrounded by an [if] shortcode whose condition evaluates to true. In other words, an [else] shortcode would not render any content, while a [eitherway] one would. You can use as many of these shortcodes as you like in a single [if] block, which gives you the ability to do things like:
<pre><code> - Am I logged in?
 [if is_user_logged_in]- Yes you are.
 [else]- No you are not.
 [/else][eitherway]- I'm sorry, what?
 [/eitherway]- I said YOU A-R-E LOGGED IN!!!
 [else]- YOU ARE NOT LOGGED IN!!! What's the matter with you?[/else][/if]
</code></pre>
A multitude of conditions are supported out-of-the-box. The following evaluate to the result of the corresponding <a href="https://developer.wordpress.org/themes/basics/conditional-tags/" rel="nofollow ugc">WordPress Conditional Tag</a>, using the no-parameter syntax:
<pre><code> is_single
 is_singular
 is_page
 is_home
 is_front_page
 is_privacy_policy
 is_attachment
 is_category
 is_tag
 is_tax
 is_author
 is_archive
 is_year
 is_month
 is_date
 is_day
 is_time
 is_feed
 is_search
 is_sticky
 is_preview
 has_term
 has_excerpt
 comments_open
 pings_open
 is_404
 is_user_logged_in
 is_super_admin
 is_multi_author
 is_multisite
 is_main_site
 is_child_theme
</code></pre>
For example, the evaluation of the <code>is_page</code> condition is equivalent to calling <code>is_page()</code> with no parameter.
<h3>Extending</h3>
The functionality of the plugin can be extended by other plugins, by means of adding custom conditions through filters. To add a custom condition, a filter hook must be defined in the following manner:
<pre><code>add_filter($if_shortcode_filter_prefix.'my_condition','my_condition_evaluator');

function my_condition_evaluator($value) {
 $evaluate=.... /* add your evaluation code here */
 return $evaluate;
}
</code></pre>
Then, you can use your custom condition like so:
<pre><code>[if my_condition]{content}[/if]
</code></pre>
A big thanks to M Miller for the <a href="http://wordpress.stackexchange.com/a/123073/39275" rel="nofollow ugc"><code>normalize_empty_atts()</code></a> function.

If Shortcode

This plugin provides an [if] shortcode to conditionally render content.

Logged In Conditional Text Widget vs If Shortcode