I just took a look at that one, I can't watch an anime movie as it just isn't my cup of tea.
OK, but just in case it changes your mind, this one isn't in the anime genre. It is animated, but it is a serious film about life and society in Japan near the end of WWII, and is highly critically acclaimed. Roger Ebert rated it one of the greatest war films of all time and one of the 300 greatest movies of all time.
From his review that best sums it up for me: "'Grave of the Fireflies' is an emotional experience so powerful that it forces a rethinking of animation. . . . “Grave of the Fireflies” is a powerful dramatic film that happens to be animated."
It is horribly sad, though, and once you see it, you will never forget it.