No Longer Here

Creates a widget that displays posts and thumbnails in a selected category. Thumbnails will display 100px square. Author name links to author page (if in use) or list of posts. Posts are sorted in descending order by date. This is a fork of <a href="https://wordpress.org/extend/plugins/category-posts/" rel="ugc">James Lao’s Category Posts plugin</a>, with less options.
Style “thumbcol” and “contentcol” classes to make it look pretty (make the thumb appear to the left of the excerpt, for example).

Featured Categories

Creates a widget that displays posts and thumbnails in a selected category.

dmikam

This simple plugin permits you to upload images to categories, tags and custom taxonomies just like to posts. 
This feature is very useful when you want to show unique image in header tor every category or even some slideshow of images. 
Also you can show a list of categories/subcategories with a little thumbnail am much more.
By the way, this plugin just uses wordpress native functionality – no aditional tables and nothing like that. 
Also it uses wordpress images so all sizes are generated automatically (custom sizes included).

WP Category Images

Simple plugin that permits to images to Categories, Tags and Custom Taxonomies.

Featured Categories vs WP Category Images