Ever since the BA crash in the early 90s, when an engine failed on takeoff, and the pilots shut down the wrong one from instrument confusion, mobile phones have been banned on British aircraft, and other countries more or less followed suit. Cell phones (mobiles, as they are called in many countries) were blamed initially, and as some say, it's guilty until proven innocent in air safety.
Now there is talk of allowing them again  . They should never have been banned in the first place. Here's why.
(As a security engineer, it's often instructive to reverse-engineer the security decisions of other people's systems. Security is like economics, we don't get to try out our hypothesies except in real life. So we have to practice where we can. Here is a security-based analysis on whether it's safe to fly and dial.)
In security, we need a valid threat. Imagined threats are a waste of time and money. Once we identify and validate the threat (normally, by the damage it does) we create a regime to protect it. Then, we conduct some sort of test to show that the protection works. Otherwise, we are again wasting our time and money. We would be negligent, as it were, because we are wasting the clients money and potentially worse if we get it wrong.
Now consider pocket phones. It's pretty easy to see they are an imagined threat - there is no validated case . But skip that part and consider the protection - banning mobile phones.
Does it work? Hell no. If you have a 747 full of people, what is the statistical likelihood of people leaving their phone on accidentally? Quite significant, really. Enough that there is going to be a continual, ever present threat of transmissions. Inescapably, mobile phones are on when the plane takes off and lands - through shear accidental activity.
In real safety systems, asking people not to do it is stupid. If it has to be stopped, it has to be stopped proactively. Which means one of three things:
If planes are vulnerable, then the operators have to respond. As they haven't responded, we can easily conclude that the planes are not vulnerable. If it tuns out that they are vulnerable, then instead of the warnings being justified as some might have it, we have a different situation:
The operators would be negligent. Grossly and criminally, probably, as if a plane were to go down through cell phone interference, saying "but we said 'turn it off'" simply doesn't cut the mustard.
So, presumably, planes are not vulnerable to cell phones.
PS: so why did operators ban phones? Two reasons that I know of. In the US, there were complaints that the fast moving phones were confusing the cells. Also, the imminent roll-out of in-flight phones in many airlines was known to be a dead duck if passengers could use their cellphones...
 To talk or not to talk, Rob Bamforth
 Miracles and Wonders By Alan Cabal
 This extraordinarily flawed security analysis leaves one gaping... but it does show that if a cellphone is blasting away 30cm from flight deck equipment, there might be a problem.