Customers can't login and can't create an account

It can be a problem in your template. You need to include form key in following templates:

1) app/design/frontend/[your_custom_theme]/template/customer/form/register.phtml
2) app/design/frontend/[your_custom_theme]/template/customer/form/resetforgottenpassword.phtml
3) app/design/frontend/[your_custom_theme]/template/persistent/customer/form/register.phtml
3) app/design/frontend/[your_custom_theme]/template/persistent/customer/form/login.phtml

<?php echo $this->getBlockHtml('formkey') ?>

Source: http://www.webspeaks.in/2016/02/magento-1-9-2-cannot-create-account-on-frontend.html

The solution for my issue was that there were two cookies

• www.shop.com
• .www.shop.com

These were conflicting. After setting the "web/cookie/cookie_domain" to "www.shop.com" there was only created one cookie, and the problem was solved.