bozdoz

<a href="https://wordpress.org/plugins/jetpack/" rel="ugc">Jetpack</a> makes it easy to add contact forms to your WordPress site, but you may want a simple way to add a <a href="https://www.google.com/recaptcha/" rel="nofollow ugc">Google reCAPTCHA</a> to prevent spam. This plugin will manipulate the Jetpack <code>[contact-form]</code> shortcode to prepend the Google script, add a button, and parse the response.
This plugin allows both reCAPTCHA v2 and invisible reCAPTCHA (see screenshots and choose whatever works for you!).
Shoot me a question about it on Twitter: <a href="https://www.twitter.com/bozdoz/" rel="nofollow ugc">@bozdoz</a>.
This plugin is open source on <a href="https://github.com/bozdoz/wp-plugin-recaptcha-jetpack" rel="nofollow ugc">GitHub</a>!

reCAPTCHA Jetpack

A simple plugin that adds a Google reCAPTCHA to the Jetpack contact form. Requires the Jetpack plugin.

Mark Jaquith

The <a href="https://wordpress.org/extend/plugins/jetpack/" rel="ugc">Jetpack</a> plugin by Automattic does something sneaky: it auto-activates new Jetpack modules. Instead of allowing you to opt in to new modules, Jetpack cheerfully activates them without your permission. These modules can change how your site works and looks.
Manual Control puts a stop to that unwanted behavior. It prevents auto-activation of new Jetpack modules.
Metal texture in the plugin header image by <a href="http://urbandirty.com/gallery/photo/2568483179-m" rel="nofollow ugc">Urban Dirty</a>.

Manual Control for Jetpack

Jetpack auto-activates new modules, without asking your permission. This plugin stops that.

reCAPTCHA Jetpack vs Manual Control for Jetpack