I tried to use Captcha at the user registration form (Core 7.2). But the Captcha does not appear, so the whole form is not working. There is an error message:

Notice: Undefined index: captcha_response in captcha_validate() (Line 557 in /www/htdocs/user/WEB/sites/all/modules/captcha/captcha.module).

Comments

Is there a CAPTCHA on the form after the failure?
Do you have some page caching mechanism enabled?

No, there is still no captcha field after the failure. Additional info: An error message tells that an incorrect captcha value has been entered (although -of course- nothing typed in).

Caching is completely disabled, and manually cleared several times (both core and captcha).

I just tried it on Drupal 7.2 and could not reproduce your problem.

Do you have other modules installed that could interfere/interact with the registration form/workflow?

I have now tried with core 7.3-dev also; same problem.

A module, that might interfere, could be Terms of Use 7.x-1.1 (buggy as well). But after disabling there is still no captcha.

Maybe Domain Access could be a problem, as it showed some errors in other context!?