With Login Failure Alert plugin you can receive email alerts when login attempt made by user is not successful. You can even set alerts only for certain usergroup(s) like send alerts only when user belongs to registered usergroup or author usergroup.
You can also send these alert emails to respective user so as to let him know about the login activity of his account.
This plugin also facilitates you to select the application where this plugin should work. Like you want to receive alerts only when someone tries to login at the backend of your site.