Seen at BoingBoing, there's a startup called MakeSpace that combines small personal storage (in units of Big Plastic Tubs) with on-demand delivery to and from wherever you are. It still costs a fair bit for delivery, though, because they're essentially offering a courier service on top of storage.
This is a business that I think will take off when flying drones take over from couriers and the post office, because it can let you rent as much or as little storage space as you need for your stuff and still get to it quickly and easily, wherever you are and at whatever time of day. If that kind of storage is quick, cheap and convenient, imagine how the world would change. Parents could keep their kids' Christmas presents out of the house and have them delivered back at the last minute on Christmas Eve (provided enough drone capacity in the system). Shoppers could wander around the city, send their purchases into storage and keep shopping, without the need to carry a lot of bags around. You can have your stuff moved between cities or suburbs automatically and never care where, specifically, it is stored, as long as it can come to you quickly. You can list it for sale online and collect payment from your buyer without the physical box even needing to move, because the tub can just be reassigned to a different owner account.
It will also save the storage industry money because they can use whatever space they need, wherever they can find it, rather than needing large, car-accessible facilities with individual lock-up doors. They can just get one big warehouse with tall shelves wherever is convenient and save the larger facilities for items that won't fit in the tubs.
Mokalus of Borg
PS - Security is obviously still an issue, though.
PPS - Especially in transit.