Nice concept, but no, this just won't happen - too many insurance risks. And if you live in a block of flats, where's it going to drop your parcel?
Sadly this is just a bit of free advertising for Amazon.

I like the idea of this delivery drone and I love to order now and receive after 30 minutes the goods. I hope that Amazon will finish this project for fast delivery.

If one comes over my field I'll shoot it out of the sky a grab the goodies (as well as the drone) !!

Well, I doubt it will work exactly as shown in the video. It will require a bit more setup than that.
How do you demarcate the landing zone?
How do you demarcate the flight path to the landing zone? Bet it works great on a clutter-free rural estate, as in the video--but what about in the city?
What about weather? N-copters are tough to fly in windy conditions. Will this ever work in North Dakota?
Still, well begun is half done. Good show, Mr. Bezos! I'll bet the demonstration didn't cost all that much, either.

I hope they can pull this off! Interesting challenges here:
a) Can this drone see overhead power or phone lines, tree branches?
b) What's to keep some kid or dog from running up and getting cut by the blades?
c) Urban areas or apartments - where to drop the package? Would this be for rural or suburban only?
d) Dependant on weather or winds?

Delivery "within a 10 mile radius of Amazon's fulfillment centers"? I guess that's Phase 1. If they can do that, then they can also deliver within a 10 mile radius of Amazon's big TRUCK, driving through cities that don't have "fulfillment centers".

I believe Bezos, The man thinks long term & BIG. His net worth is 25 billion...you don't get that rich by thinking small.
Drones are the future, in a few years from now they will be common place. Projections are saying that by 2017 there will be 7500 drones over the US, a number which will grow extremely quickly once they get it working smoothly, and all the regulations ironed out.

It's a publicity gimmick that will never happen.

The drones need to be helicopters, not quad/hex/whatever copters, and the entire thing (blades and all) need to be soft (inflatable probably) and powered by tip-mounted shrouded ducted fans - then this might work.
Or in laymanspeak - these need to be able to crash into anything (eg: a humans face, a car windsheid, a horse), and never hurt anyone or anything, ever.

It is possible to use solar powered airships (solar panels in airship balloon) for transport the packages. Less energy consumption, less pollution.