If you don’t want WordPress default recent posts widget to show all categories then try this widget plugin, using it you can show recent posts on your sidebar widget from selected categories.
Posts in checked categories plugin adds a widget in your blog’s sidebar that shows the most recent posts in categories you have checked. You can add multiple widgets like one showing categoryX recent posts and other showing categoryY recent posts and so on. You can also set the number of posts to show, you can change the order of posts and a few more features you get in this widget. All you need is install, activate this plugin then add its widget to your blog’s sidebar.