datagutten

The project is inspired by RDP Wiki-Press Embed by Robert D Payne. Some code is also copied (noted in source).
The difference is that this is simpler. It contains as little CSS as possible to be able to customize it for each theme.
Links are rewritten to make the users able to navigate in the wiki without leaving your wordpress page.
The text on the wiki image page will be added as a title=”” tag to the image in wordpress, so by using the plugin <a href="http://archetyped.com/tools/simple-lightbox" rel="nofollow ugc">simple-lightbox</a>, the text will be shown below the image in the lightbox.
It is developed for use with a private MediaWiki install, but it might work with wikipedia as well.
<h3>Tested themes</h3>
Virtue: Works well 
WP-Forge: Works well 
Twenty Ten: Trouble with image alignment 
Twenty Thirteen: Works well 
Twenty Fourtenn: Trouble with image alignment, pages get very narrow 
Twenty Fifteen: Trouble with image alignment

Wikiembedder

Embed MediaWiki in a wordpress site and allow users to navigate the wiki without leaving your wordpress page.

oltdev

This plugin enables page or post authors to scrape content from mediawiki pages and appending it to their pages. 
It works by scraping content from mediawiki pages by going to a special mediawiki page url.
For example http://en.wikipedia.org/wiki/Wordpress?action=render
The content rendered on the final page or post will always be the newest content, however it is not searchable via regular WordPress search form.
Use case: 
This plugin is great for adding documentation to your site. 
Since wordpress.org is using mediawiki for the codex you could potentially display wordpress codex pages on your site without much effort, just enter the full url of the specific wordpress codex page.
Enjoy

Wiki Append

Append a mediawiki page at the end of the regular wordpress page.

Wikiembedder vs Wiki Append