These days most Anime get me (with exceptions being there), but I don't completely cry for some reason, it's like tearing up a bit and then watch it again as if nothing happened.
The anime which actually made me cry was Kimi no Suizou wo tabetai (I want to eat your pancreas)
Small spoiler alert below if you are going to watch the movie in future.
The part where I cried was the main Haruki asking "Are you really dying" and Sakura replied "Sure am" and that with a bright sweet smile, so yeah it got me, and I started crying, for real. It was midnight and I started weeping crazily.
You can check the anime
here on MAL. It's pretty well known but just incase if anyone didn't knew