[These are Frequently Asked Questions about the current state of UAV regulation in the US. Regulations elsewhere are different, but here is a similar post giving the rules for Canada.]
Q: Are UAVs legal in the United States?
A: Under certain conditions, they are. There are two ways to legally fly Unmanned Aerial Vehicles in the "National Airspace", which is to say all but certain restricted areas: 1) Get a Certificate of Authorization (COA) from the FAA, a process that can take months or more. 2) Fly under exemptions granted to non-commercial ("recreational") flyers who adhere to certain restrictions. More detail is here.
Q) What are those restrictions for non-commercial UAVs flying without a COA?
A: You MUST do the following: 1) Stay below 400ft. 2) Maintain a "pilot in control", which is to say that you must always be able to take manual control and fly the aircraft out of danger (in general, that means maintaining line-of-sight contact with the aircraft). 3) Stay away from built-up areas. More detail is here.
Q) Who can apply for a COA?
A: Typically only government agencies (Law enforcement, Civil government, etc). This is not an option for a private individual.
Q) I've heard that the FAA doesn't allow unmanned aircraft with cameras and/or GPS. True?
A) No. Commercial use of aircraft with cameras is regulated as above, but aircraft flying under the recreational exemption may use cameras and GPS.
Q) What countries have more relaxed UAV regulations?
A) Australia and New Zealand are famously progressive in their UAV policies. Other countries, such as Mexico, have been know to be relatively friendly, too.
Q) What are the prospects for FAA regulations that allow amateur UAVs more freedom?
A) There is currently a rulemaking proceeding that aims to improve the regulations on UAVs. It will take a while; indeed, you shouldn't hope for anything before 2010-2012. There may be a special category for UAVs under 4 pounds, which may be more lightly regulated. But then again there may not. It's all up in the air, so to speak, and the forces that oppose amateur or commercial UAVs in the National Airspace are many and powerful. Speak up!
Q) What about universities and other students. Any exemptions for them?
A) Not automatically. But they may be able to get COAs more easily if they are federally funded and go through that agency.
Q) What if I break the rules?
A) Well, for starters, we don't want to hear about it here! We realize, of course, that people break the rules all the time on the assumption that if they use good judgment and stay away from built-up areas, they won't be caught. That may indeed be the case, but it will only take one cowboy flying a UAV into an airport landing zone and endangering civil aviation to set our hobby back by decades. So please don't do it! (Plus you could go to jail)
Q) Okay, I'm obeying all the rules. Are there any other guidelines for safe and responsible UAV operations?
A) Yes. RCAPA (the RC aerial photography association) has some excellent guidelines that are a great place to start.