I decided to use the NoCaptcha ReCaptcha plugin on my site (https://www.seblod.com/store/extensions/48177). When I push the website to my webhosts server the captcha kept failing although it didn't in my development enviornment.
I debugged a bit and noticed the file_get_contents() method the plugin uses for Recaptcha response relies on the php.ini parameter allow_url_fopen to be set. My webhost controls the php.ini settings.
To fix the problem, I changed the plugin to use cURL instead.
If you encounter the same problem/this plugin not working it is probably the same issue, especially if you have allow_url_fopen unset.
To fix it open db_no_captcha.php (plugins/cck_field/db_no_captcha). Find line (around line #154):