Some numbers about videos:
When that time comes, Pixar's render farm will have to go through another massive growth spurt. And so will its storage space, which Whitehill estimates already exceeds five petabytes, or 5.4 million gigs.
Science experiments, like LHC, are producing gigabytes of data per second. Astronomy can also give you more data than you can handle.
The most likely demand for space at home comes from backups. This includes backups of your computer storage, and backups of your DVDs (in case they get scratched.) It is very appealing to have an endless history of your filesystem that goes back for years. You can then access any file that you used to have on the box, even if you deleted it a year ago and only now (at tax time) realized what have happened.
Well just from travel we have almost 3 Ts filled on a external HD, but yeah that makes sense.
Movies, scientific experiments and of course all the Target store customer files as well...