I have a 2Tb Iomega nas device which attaches to my lan. Iomega is now owned by emc2/Lenovo. There is cloud software which allows me to access it from anywhere on the Internet though it doesn't like 3G connected devices. Too many proxies to allow IP resolution.
The software is available for Windows, Mac & Linux plus there are Apps for Android & iOS devices as well.
I can also access it from my hard wired (cat5) blueray player to watch videos I've ripped down using handbreak.