I know that passengers are asked to put their cell phones on flight mode. But some carriers allow use of WLAN on-board. So, what radios should passengers refrain from using? Also, if a person uses a GPS receiver on his/her mobile phone (on flight mode), would it interfere with the aircraft communication system?
There is actually a simple answer, but it probably isn't exactly what you are looking for: Refer all questions about what is allowed to your specific airline.
Each airline has to come up with their own list of allowable electronic devices, and submit that list to the FAA with appropriate documentation in order to gain approval to allow passengers to use them during flight.
Some airlines allow almost everything as long as it can be put into a non transmitting mode (airplane mode), while some still require ALL electronic devices to be completely powered down at all points during the flight.
Because of this, every airline is a little different and you are required to follow their rules while on their flights.
The GPS receiver would not cause problems, but this doesn't mean that you are necessarily allowed to use it, and there are other things in your phone that could cause a problem though.
In general, no electronic device that has a transmit function may be used because of possible interference though, unless specifically approved.
The simplest answer to your question is, none that have not been specifically approved for use by the FAA. The FAA, in U.S.-controlled airspace, has pretty much all the power and responsibility for ensuring civilian air travel is safe, and they operate with an abundance of caution in all things, because that draconian code of rules and regulations is what keeps the agency itself from taking blame for a plane crash; if everyone followed all the rules and the plane still went down, it's the government's butt on the line.
So, the FAA has, for decades, maintained more or less a blanket ban on operation of devices with a transmit feature, even as modern airframes (and by "modern" I mean practically anything in the sky today) are well-shielded against radio interference, and consumer devices available for purchase and casual use do not transmit on frequencies anywhere near those used by aircraft for communication or navigation. The reason is simply that it is possible for a device to cause interference with aircraft systems, whether directly by pirating the frequency or indirectly through intermodulation or other artifacts of radio carrier wave dynamics, and it was simpler, easier and cheaper at the time for the FAA to ban them all than to evaluate every device or device type against every airframe in commercial aviation, verify empirically that it does not cause interference, and educate flight crews and the general public about which device types, makes and models specifically are or are not allowed.
The FAA has since changed tack; it has worked with the FCC beginning in the 90s to develop a set of joint rules for both device and aircraft systems design that, if complied with by the manufacturers, will guarantee the device will not cause interference. Devices meeting these criteria, including practically any smartphone or tablet on the market today, can be used during "non-critical" stages of flight (all usage of potentially-interfering devices is still restricted during takeoff, landing or at any time by instruction of the flight crew) while onboard an aircraft certified for use of such devices while airborne (meaning the airframe complies with rules for shielding/isolation of sensitive electronics; this certification, including any needed retrofits, can be done during scheduled maintenance on each airframe).
@PriyankGupta was heading in the right direction. Back when more people carried portable FM/AM receivers to listen to music, there was a problem with the receiver local oscillators causing interference. For example, If I wanted to listen to an FM station at 105.1 MHz, the local oscillator was 10.7 MHz above that frequencies so it was operating at 115.8 MHz. Leakage from the local oscillator could and did interfere with the aircraft receivers operating in that band. Of course, now days, almost no one uses portable FM broadcast receivers. However, the concept is the same for the various types of receivers and transmitters. The radios themselves may not interfere directly but one of the signals that gets mixed with another signal might. In modern commercial aircraft, they have multiple different systems so the likelihood of an airplane being severely compromised by a cell phone in the passenger section is very small but not zero. I always turn mine to airplane mode. I don't my family reading in the newspaper that the cause of a plane crash I was killed on was my cellphone being on.