Around the same time the Joomla 2.5.16 / 3.2 update came out ReCaptcha stopped working.
While it might seem the update caused the problem, it was Google's change of url that did it.
http://api.recaptcha.net is now http://www.google.com/recaptcha/api
This problem will probably be addressed in Joomla 2.5.17 / 3.2.1
To fix manually:
In plugins/captcha/recaptcha/recaptcha.php line 24
replace
const RECAPTCHA_API_SERVER = "http://api.recaptcha.net";
with
const RECAPTCHA_API_SERVER = "http://www.google.com/recaptcha/api";
or use the link below to download a repaired version of the plugin from third party site seepeoplesoftware.com
Download a fixed version of the Recaptcha Plugin for Joomla 2.5.16 / 3.2
Install using the Extensions Manager (no need to uninstall first)