I'm not getting this to work at all.

My settings:

for Joomla

In Joomla back-end (1.5.10)
Site->Global Configuration->System:
User Settings:
-Allow user registration: NO
-New User account activation: YES
-Front-end user parameters: HIDE

in CB (1.2.1):
CB Configuration Manager->Registration->Allow User Registration: yes, independently of global site settings.

With the above I got a 403 error (not allowed). Could this be because of SEF or ...I cannot figure out to be honest as it seems my settings are correct.

It's nice that you gave us some info about your setup, but I feel there is more info to be given still.

It sounds like your error is a 403 error. I don't think SEF is the cause.

What I am curious about is what the URL is for the 403 page?

i have a similar error - with the same settings as you.

Following registration, the confirmation email is sent however on clicking the link

www.jap-mart.net/index.php?option=com_comprofiler&task=confirm&confirmcode=

I receive the error:

You are not authorized to view this page!
You need to log in.

If you goto Administrator > Extensions > Module Manager, can you see if any of your CB modules are set to Public or Registered.

Also, it looks like your URL is missing the confirmation code.

Have you established a public menu link to Community Builder User Profiles (mandatory!)?

All the settings were as per the instruction guide yet the things did not behave as expected but, because the CB looks quite good on my website I'm going to give it another chance.
At the moment I've managed to uninstall and I'm going to go through the installation routine once again.
The only thing I can think of is this one: At the beggining of installation I didn't set up the permission for the user registration (or something like that) "Public" as directed in the installation guide (missed that paragraph) and this might be the problem.