Without throwing a wet blanket on things, there are a few practical and legal considerations you may need to be aware of. Most of this has come about since quadcopters in particular are relatively easy to fly, and are now a popular items for all ages. These first timers may be simply flying for the joy of it, without considering the possible impact of an unexpected crash or loss of control of what ostensibly is a harmless toy.
The Legal Stuff:
There are some (rather confusing) FAA requirements regarding flying remote controlled aircraft of the drone type, which essentially boils down to three "tiers".
1 - hobby or toy devices weighing less than 0.55lbs (about the weight of two sticks of butter) are currently not subject to registration with the FAA and you can fly them subject to common sense and local ordinances.
2 - hobby or toy devices weighing more than 0.55lbs (that is, most camera platform type quads) are subject to FAA registration and failing to adhere to the laws affecting those types of aircraft may result in hefty fines and or jail time (!).
3 - drones used for commercial purposes are subject to additional requirements that can become pretty intense, including requiring the "pilot" to obtain a modified form of pilot's license. Yes, really.
Here is a great site to assist with the legal stuff. www.dronelawjournal.com
The Practical Stuff:
Micro or mini drones, such as the Hubsan X4 that I have, can be flown indoors and outdoors. They are small and light as the name suggests, and have a limited control range of maybe a couple of hundred feet.
While they can travel quite quickly, and the spinning props might break the skin, they weigh just a few ounces and usually come with prop guards and would likely not cause any notable injury if they collided with someone wearing everyday clothing.
Even so, would you like to be sitting on the beach when out of the blue something smacks into your head and gets tangled up in your hair? No, me either - although I would like to have hair that could get tangled...
The larger models have larger, faster spinning props and could cause cuts and bruises under the worst case scenario. Actual commercial-type camera drones are not something I would want to fall on me.
So, the common sense rules for flying remote control quadcopters (or most other flying craft) would be along these lines:
1 - don't fly over or at other people (so don't fly downtown!)
2 - don't fly over public roads or highways
3 - don't fly within 5 miles of an airport (FAA requirement)
4 - don't fly over 400ft above ground level (FAA requirement)
5 - don't fly near cell or microwave towers
6 - don't fly the quad out of visual range (even if you have a camera on the quad that lets you "see" where it is going)
You should also be aware of "no fly" zones around sensitive areas or government facilities, there are several smartphone apps that allow you to check before you fly, such as the aptly-named B4UFLY.