If you're using phpBB, then yup, phpBBHacks has something like that - I'm pretty sure of it. If not, just go to the register page and view the HTML source code. Copy the <form> and all of the textboxes, etc. in between. Then, just paste that data (the required fields) on your homepage :)
vBulletin version 3 has a quick registration form as default.
The admin can pre select the default options and setup required fields (if any are needed)
But a user can enter a user/pass and email and is signed up. (if email verification isn't turned on).