Alright, fair enough. I just reinstalled Ninja Forms and tried again, turns out I am partially to blame myself.
Apparently I forgot to set an administrator email address (I figured it would just use the site admin email). Ninja Forms did not give a warning about this, and I could fill out the form on my website without problems, except no email was sent. Seems really strange to me.
During my first install (after which I rated the plugin), when I submitted the form using AJAX, I ended up at a white page showing nothing but a JSON object. Without AJAX submission, I got a white page that just said 0.
This did not happen during my second install, but might be something you could look into.
All in all, my initial reaction turns out to be too harsh. Once you have read this message I will remove my 1 star rating.