In the Global Configuration, you can set the parameter Allow User Registration to No. This will prevent from the Register option from showing.
As for as password resetting is concerned,
(a) if you are using the login module, you can edit the file default.php located in the directory \modules\mod_login\tmpl to remove the forgot username and password forgot options.
(b) if you are using the login menu item, you can edit the file default_login.php located in the directory \components\com_user\views\login\tmpl to remove the forgot username and password forgot options.
As you will be changing the core Joomla! files, it is recommended that you follow the override technique as documented at
http://docs.joomla.org/How_to_override_the_output_from_the_Joomla!_core.