This is a question that generates a lot of comment and confusion on the newsgroup,  but few people have the necessary experience to give an answer based on reasoned engineering experience.  Here are my answers and comments.

1)  GPS Receivers are known to radiate RF energy from the oscillators and computer logic circuits inside the GPS.  Won't this possibly interfere with the navigation equipment on airplanes?

Answer:
Every electronic device with a computer or oscillator inside radiates *some* radio frequency energy.  The key word is *some*.  A cellular telephone,  ham radio transmitter, business band radio transmitter,  CB radio or similar transmitting device is DESIGNED to radiate significant amounts of RF energy.  They *DO* have the potential to interfere with various Avionics equipment and SHOULD NEVER be used on board an aircraft during flight.  Many airlines prohibit their use at all times while on board a commercial airliner.

With other electronic devices, such as laptop computers,  electronic games,  AM and FM Radio receivers,  and the like,  the answers are not so black and white. There are documented cases of AM/FM radios causing interference with Avionic systems and as a result,  AM/FM radio receivers are generally prohibited.  Most electronic games are cheaply built and do not have the same FCC mandated  requirements for shielding as do other electronic systems such as computers and GPS receivers..  Even though these game devices are low power,  they have been accused of interference with Avionics during the terminal navigation phase and so are prohibited except during cruise (typically above 10,000 feet).  Laptop computers are now in widespread use by passengers in airplanes.  While these devices are relatively high overall power consumption (in the 10 watt range) they are generally well designed,  with adequate shielding.  As a result,  laptop computers are allowed to be used during the cruise portions of virtually all passenger airline flights.

Well then,  What about GPS Receivers?

GPS receivers are very low power devices.  The typical TOTAL energy used is less than a one watt rate.  If all of this power were converted to RF,  then there WOULD be a problem.  However,  the fact is that a) only a very tiny part of this energy is capable of being converted to power that *might* generate RFI and b) the designers of GPS receivers are required to consider RFI during the design so that the finished product passes FCC Part 15 Class B (residential) EMI (Electro Magnetic Interference) tests.  (Note:  Contrary to some people's intuition,  Class B (residential) EMI testing is considerably more stringent than Class A (Industrial/Commercial) EMI tests.  This is because in residential situations,  a neighbor may be just 10 feet away whereas in industrial environments, neighbors are usually further away.)  c) By design,  (or happy accident),  the "spurs" generated by a GPS generally fall outside the communications frequencies used by Aircraft and so have not been a problem even though a few "spurs" exist.  (If no one is listening on a frequency where a potential RFI signal exists,  then there is no interference.)

What is the TRACK RECORD of GPS receivers in so far as EMI is concerned?  Garmin and Magellan tell us that there has never been a REPORT of any problem caused to any avionics system as a result of the use of a GPS on an aircraft.  No pilot or engineer on the GPS newsgroup has ever reported a GPS receiver causing interference to an avionics system on an aircraft.   About 80% of the airlines in our survey permit the use of handheld GPS receivers by passengers.  I believe it is safe to say,  "If EMI from a handheld GPS were a problem *somebody* would have noticed it by now".  My conclusion therefore is that the use of a low power GPS receiver on an aircraft is substantially less likely than a laptop computer to generate significant amounts of EMI and since laptop computers are judged "safe" then GPS receivers are "safer".

2)  But SOME airlines do not permit the use of GPS receivers.  Why is that if they are "safe"?

Answer:
Some safety officials are more cautious than others.  Some are less technically competent than others.  If there is a "potential hazard",  no matter how insignificant,  it is always easier to say "no" if you have no basis for a decision.  In the case at hand,   to say,  "yes, it is safe to use a GPS on board an aircraft"  requires a substantial amount of technical knowledge and expertise in a complex field.  To say "no" you cannot use a GPS on board an aircraft requires no such skills and is "safe" in many contexts..  (Note:  One aviation industry EMI expert who reviewed this material  suggests that my reasoning above is overly harsh. He states that *some* safety experts are fearful that some FUTURE Avionics equipment may incur harmful interference from a GPS and once the GPS "barn door" is open,  it will be difficult to close it.)

3) If a GPS is safe,  why can't I use it on an airplane anyway,  even if the pilot says NO?

Answer:
This would be a) unwise,  b) illegal and c) dangerous.  Never presume that you have more authority than the Captain of a ship!  He is responsible for the lives of his passengers and likely has  knowledge and experience about his aircraft and/or equipment and/or this particular flight that no one else has..  The use of a GPS by a passenger is NOT worth a confrontation and a possible visitation from the police or FBI when you land..

4) I have used my GPS during takeoff and landing and nothing happened.  Why can't I keep doing it?

Answer:
Takeoff and landings are the most dangerous parts of a flight.  Even though the likelihood of an EMI problem from a GPS receiver is low,  there is no reason to take a chance on interference with a critical system during a critical moment during takeoff and landings.  The life you save could be mine (and yours).

5)  You are WRONG!  I put my GPS a foot or two from my scanner and I can hear "spurs" at several frequencies.  Therefore,  the GPS CAN cause EMI problems.

Answer:
Yes,  you can hear a "spur" at some discrete points with a wideband scanner.  However,  these "spurs" are very low power and the typical scanner receiver is not well shielded.  The energy thus radiated can only be DETECTED a few feet away and a) such signals will not normally cause problems with communications receivers since the signal energy dissipates as the SQUARE of the distance between the radiator and the receiver.  Probably the main reason why these "potential" RFI signals have not been a problem is that these "spurs" have not been found to fall on frequencies used for aircraft navigation and communications. Such "spurs" have the "potential" to cause problems,  but due to the small signal levels and the frequency of the GPS receiver spurs,  they have SO FAR not been a source of interference to Avionics systems.   (Again:  If they HAD been a problem,  someone would have noticed.)

The BOTTOM LINE (According to Joe)

The interference potential of handheld GPS receivers is minimal.  However,  no passenger should EVER operate a GPS receiver on board an aircraft except in strict accord with the directives of the flight crew. 

Now as to FAA rules and regulations:

http://www.airweb.faa.gov/REGULATORY_AND_GUIDANCE_LIBRARY/RGFAR.NSF/0/5D4AEFD672582D15852566CF006135DC?OpenDocument

Joe Mehaffey