I use a NAS (Synology DS111). I can access it within, and out, my network.. Not really the cheapest set up (NAS can range from $150 + cost of HDD), but keep in mind they are typically feature rich.
If you don't really have a need for the full functionaltiy of a NAS there are routers that have this feature. Netgear's line calls it ReadyShare. It allows you to connect an external drive via usb and makes it accessible within your network. And in some case, outside as well.