Hi to the community!
Let me present you the module I created for displaying members registration form within EE templates.
The only options before to customize registration page were either to modify EE specialty templates (and in most cases you could not get exactly same design and look, and no EE tags are functioning there) or User module (which is is rather overkill for such simple feature, especially having in mind its cost).
Now you can simply build the form using {exp:sa_member_register:form} tag and place it anywhere.
So say welcome to Stand-Alone Member Register. The module is available both for EE 1.x and 2.x
You can get it from Devot:ee for just $7
UPDATE
I have just released Stand-Alone Member Edit! Consider using these two together 😊