JohnnyPea

This plugin adds registration date and last login date columns on the “Users” page. 
It also checks whether user logs in within 30 days after the registration if he does not his account is deleted – this option is disabled by default, you can change this settings on Check Last Login Settings page in Settings menu.
WARNING! The plugin is not updating the login time when logging through stored login cookies.
I am open to suggestions to improve the plugin !

Check Last Login

Simple plugin which checks user's login status and displays registration date and last login date columns on the "Users" page.

kostikpenzin

En: 
This plugin will automatically login your new user after the registration process. General scheme of authorization and registration is not changed. 
I will be glad comments and observations.
Ru: 
Этот плагин для автоматического входа нового пользователя после регистрации. Общая схема авторизации и регистрации не изменена. 
Буду рад комментариям и замечаниям.
Author: Penzin Konstantin
Site: <a href="http://pkweb.ru/" rel="nofollow ugc">PKweb.ru</a>

Auto Login User on Register WordPress

This plugin will automatically login your new user after the registration process

Check Last Login vs Auto Login User on Register WordPress