Shigofumi is the story of Fumika, a mail carrier from a realm called Shigo. However, the letters she delivers aren't normal letters, of course. Fumika delivers shigofumi, letters sent by the deceased carrying the words they couldn't say before. The story follows Fumika as she delivers each letter to its recipient.So... it sounds boring as molasses, doesn't it? Well, it probably is if you like fast paced action anime. However, if you loved Jigoku Shoujo or stories like it, you'll like Shigofumi, since it's basically the same premise.
The demographic isn't really clear all I can find is that it's targeted at males, but it has the feeling of a seinen anime, or just a mature shonen.
The anime spans 12 episodes and one OVA, and although it's pretty confusing at first, you'll get the idea by episode 2. There's an overlying plot, but the true stuff isn't really revealed until a couple episodes in. So, beware, don't drop it prematurely.
There are some sad stories in Shigofumi, especially episode 10. It has it's funny-ish moments... enough to get a small smirk out of you at least. But other than that, it seems serious, and somewhat sad. Despite the sad parts, you see everyone get a happy ending in the OVA.
The animation and character design aren't anything flashy, but and I think it's quite nice except for Fumika's eyes. But, I suppose it gives her an un-human, otherworldly appearance.