I've got one, I've got a 2TB collection of data that I regularly syphon files from when I am traveling. It is easy and works great, I don't need to leave a PC running (draining my wallet through the power company) to access all the data since it is a low-power device. It is as fast as my internet speed and costs nothing for the service.
I built a fanless Core i3 Ivy Bridge machine that, according to my Kill-A-Watt, uses about 10W unless its really cranking out some computations for me. It runs an L2TP over IPSec VPN server that allows me to remotely connect to my machine from any device, including my iPad or phone. I have a virtual machine that runs a linux file server on it, and one that runs a windows host for RDP. I was originally running all of this on one of the original Atom boards but I found myself in need of upgrading.
The overall cost of building the computer from scratch was around $400 (Motherboard, CPU, RAM). I repurposed an existing SSD for its boot drive (Intel drive that uses 0.125W), and then a 1TB mechanical drive for storage. My off-the-top-of-my-head calculations put my electricity cost at about $11 a year.
I use ZoneEdit for DNS services and my router automatically updates the IP address the moment that it changes. My ISP changes my IP address about once or twice a year. I spend about 2 hours a year on security updates and other system maintenance.
Why did I set up a system like this with RDP capabilities? I used to spend a lot of time in hotels and I do not trust hotel WiFi. I'd also travel internationally and could not always access the services I wanted to access remotely. I sometimes used the VPN connection to buy products at a better fair (did you know that British Rail gives you a better price on train tickets if you purchase from the US instead of the UK?). Most of all, I have a secure network with which I can do all of my online banking, emailing, and bill-paying while on the road. I maintain a similar box at my parents that I use to remotely administer and repair their computers from across the world (assuming they can boot them). Totally worth it to have a real machine, IMHO.