At the moment, we don’t plan to support reCAPTCHA.
Instead, we have full support for our own anti-spam plugin https://ww.wp.xz.cn/plugins/akismet/ which transparently checks your comments and contact form submissions against our own learning global database, rather than forcing folks to click images to identify planes, trains, and automobiles. 🙂
The database is quite vast and learns from spam trends contributed by millions of Akimset users every day (when they highlight missed spam or false-positives), so it should be rather comprehensive. If not, just click that “Spam” link in the notification so that Akimset can continue to learn.
If Akismet is still not performing up to specs, please let us know at https://akismet.com/contact/
I’m sorry, I realized this morning that I only answered about reCAPTCHA with regards to comments. The above is still true, of course, but only for our Comments module.
Elsewhere however, you can add reCAPTCHA for our email sharing button following the guide at https://jetpack.com/support/sharing/#captcha
We are also working on adding reCAPTCHA support to our contact form (which is also protected by Akismet) https://github.com/Automattic/jetpack/pull/9389 but until then, there are two third-party plugins: https://ww.wp.xz.cn/plugins/recaptcha-for-jetpack/ and https://ww.wp.xz.cn/plugins/recaptcha-jetpack/