There appears to be a view for the registration form that comes with Expressionengine 2, but modifying it does not appear to do anything for the front end. That file is /system/expressionengine/views/members/register.php.
Where can the new user registration form be altered?
Thanks in advance.
The front end template is /themes/profile_themes/(your selected theme)/registration_form.html
You can edit this in EE via Design -> Themes -> Member Profile Templates.
I can't explain why these are static HTML files when most templates are stored in the database.
A tiny bit more info at http://ellislab.com/expressionengine/user-guide/cp/design/themes/member_profile_templates.html
The problem with using this is that you get the rather shoddy EE validation system - a separate page with the validation messages, from which you have to go back (!) to correct your input. They're also served up with their own header (html_header.php) and footer (html_footer.php) and inline styles (stylesheet.html), though you can use template tags and snippets etc. in them.
IMHO you're better off writing your own templates or using a plugin.