Brandon

This plugin is now deprecated, please use WordPress Access Control for access to new features, such as restrict to members or non-members, restrict to certain roles and specify a redirect URL. This name didn’t suite the version 2.0.
https://wordpress.org/extend/plugins/wordpress-access-control/
This plugin allows you to mark a page as “Members Only”. Once this is done, the user must login to view the page. However, you can still add the page to the menu, and it will then ONLY show up if the user is authenticated. That way you can have more items for logged in members on your website.
This plugin is designed for people using WordPress as a CMS. It’s extremely easy to use. You install the plugin, and activate it. Whenever you create or edit a page there is a checkbox on the sidebar that allows you to mark that page as members only.
This plugin now fully supports wp_nav_menu and wp_page_menu for older sites, so it should be compatible with older versions of WordPress, as well as wp_list_pages for certain themes.
It automatically sets the walker class to the one we custom made so theme developers don’t need to do anything

Members Only Menu Plugin

This plugin allows you to mark a page as "Members Only" and still add it to menus (Only visible if logged in)

nestwiderhaken

Shows only posts, that are newer, than the day the current logged in user was created. 
This plugin is only useful if you have an other plugin installed forcing any visitor to login first. 
In that combination you get a blog in which the posts of older users are invisible for new users. 
None of the old users must therefor worry about statements made in older posts becomming available to users he don’t want. 
In the moment a user publishes a post, the amount of authorized readers for this post stays the same.

Only New Posts

Works fine.

Shows only posts, that are newer than the day the current logged in user was created.

Members Only Menu Plugin vs Only New Posts