In all Truth Naruto Shippuden is the only anime that actually made me full on cry and it was only like two episodes. Anime: Your Lie in April I can easily say this is one of the saddest animes I've ever seen (not including horror because I just expect horror to be sad) The story itself is a beautiful tragedy and is really enjoyable. Its definitely worth the tears. When i watched this anime I was going through a rough patch and so there wasn't really anything that could make me cry though there was a few times my eyes stung. I'm pretty sure if i watched it now I'd cry.
This video shows a glimpse of what Kousei is being tormented by.