If you have a lot of data -- photos, movies, backups, or other files -- a home server is a great way to keep them all in one place for use throughout your house. The Fractal Design Node 804 is my choice for a good-looking, functional PC case for a DIY home server.
Sure, you could buy a Synology or other NAS enclosure, and they'd probably be smaller -- but nothing gives you quite the flexibility of a PC you built yourself. You can go as cheap and low-power as you want by buying old parts no one wants anymore, and install just about anything on the operating system of your choice.
The problem is, most PC cases are either big traditional towers, which are an eyesore, or they're small with no room for hard drives. If you're just building a small server, that's fine, but over time, you may find that you want room for expansion (my home server is up to five hard drives now).
That's where the Node 804 comes in: it's a microATX "cube style" case split into two sections. On the left side, you have your motherboard and other components, with room for two hard drives. On the right side, you have your power supply, cables, and two racks of up to eight hard drives, so you can expand to your heart's content. And, while it isn't exactly "small", its cube-style shape makes it easy to fit in an entertainment center (like mine, pictured below on the right) or a closet somewhere. And while $145-160 may seem expensive, it's actually very decently priced for the quality -- and much cheaper than comparable server cases with hot-swap bays or a dedicated NAS like a Synology.
Of course, you get what you pay for in that sense -- swapping out hard drives isn't as easy as dedicated server cases, and it's bigger than a Synology would be. But as long as you have the room for it (and the patience to open it up when you add new drives), it works great.
If you can live with fewer drive bays, the Lian Li PC-Q08B is a good, smaller option that costs about the same -- but it only takes Mini-ITX, so make sure your motherboard has enough SATA slots for those drives.