Another possibility would be overloading the customer/account/create action and just redirect the user to the home page when this action is invoked.
In a first time, just do what was proposed by Ben V. It will remove the possibility to view the registration page.
Then, create a new module in which you will overload the AccountController.php.
1- Create a new folder in app/code/local/ named Mycompany
2- Create a new folder in app/code/local/Mycompany/ named Registrationremove
3- Create app/code/local/Mycompany/Registrationremove/etc/
4- Create app/code/local/Mycompany/Registrationremove/etc/config.xml
Copy and Paste in config.xml :
<?xml version="1.0"?>
<config>
<modules>
<Mycompany_Registrationremove>
<version>0.1.0</version>
</Mycompany_Registrationremove>
</modules>
<global>
<rewrite>
<mycompany_registrationremove_customer_account_create>
<from><![CDATA[#^/customer/account/create/$#]]></from>
<to>/registrationremove/customer_account/create</to>
</mycompany_registrationremove_customer_account_create>
<mycompany_registrationremove_customer_account_createPost>
<from><![CDATA[#^/customer/account/createPost/$#]]></from>
<to>/registrationremove/customer_account/createPost</to>
</mycompany_registrationremove_customer_account_createPost>
</rewrite>
</global>
<frontend>
<routers>
<registrationremove>
<use>standard</use>
<args>
<module>Mycompany_Registrationremove</mIn the above example structure, the controller class name should be changed from
class Mycompany_Registrationremove_AccountController extends Mage_Customer_AccountController
to
class Mycompany_Registrationremove_Customer_AccountController extends Mage_Customer_AccountController