I'm sure it happens (the post a bit back about the guy's laptop that was broadcasting mic input due to wacky wiring is a great example), but I'm really dubious that it's significant enough to actually interfere with comms from a system designed to throw radio signals 200 miles.
Sometimes you hear interference from GSM phones because the TDMA time divisions are in the AF range, but that's really a function of the power envelope rather than the power of the transmitter. I don't even really count this because I've never seen a GSM phone interfere with a non-part-15 device. Radios have to reject nearby signals; noise well outside their frequency range is even easier to reject. (I've never heard anything like GSM interference while operating my HF radio, either, and I have a GSM phone.)
These are local nav systems, not FM stations that put kilowatts into the air.
Take an ILS (instrumental approach) frequency 108Mhz. Any piece of wire of around two feet (half dipole) can be a pretty effective antenna at that frequency. Say, headset cable + an output cascade of the amplifier self-excited at this frequency? Doesn't happen in real life, but still...
I am not sure how much effect this has, but it's something to keep in mind.
And although it is not a problem for a pilot in normal conditions, it could be a factor that complicates things for a pilot. If the visibility on a takeoff/landing is bad, there is traffic congestion, air traffic control is stretched to the limit you'd definitely don't want a faulty cell phone suddenly jamming an ILS approach system ;)