I want to get email notifications to the portal email address whenever a new user joins the portal.
My guess is that I should code a new product to do that.
Does such product already exist (for Plone 4)?
I checked content rules, but AFAICT it could work only if I made the users contentish themselves with something like membrane/remember, but for my requirements that would be overkill.
If you want to do it the right way, follow Martijn's directions above.  If you want another dirty solution, do the following:

make a copy of register.cpy
insert the following code:
context.MailHost.send('Content-Type: text/plain\n\n' + 'User has registered: ' + str(username),
            mfrom='me@gmail.com',
            mto='you@gmail.com',
            subject='User Registration',
        )
Is there an easy way in Plone to get email notifications when new users join the portal?