I haven't watched much anime in my life, but one anime that I did watch a long time ago that I still love to this day is called "The Secret World of Arrietty".
That's always a tough one for me, I've watched hundreds over the years but one that I have actively sought and even bought the release of a couple times is called Saikano or She the Ultimate Weapon. It's a pretty heart wrenching anime but I think it hits home with how we, as humans, would react to a world being torn apart.