We really have to restrict any answer to UK airports because laws in overseas countries vary and there is no doubt that in some countries it's asking for trouble to produce a camera inside an airport.
In the UK the simple answer is that it is unlikely to constitute a criminal offence unless, for example, it's done to harass someone. However, in these days of heightened security don't be surprised to be checked by the police at the airport if they have any suspicions at all about what you are doing and in some cases if they haven't. The worst scenario could be arrest on suspicion of being involved in terrorism, though this is highly unlikely to happen to the bona fide airport plane snapper.
UK civil airports are not regarded as prohibited places under the Official Secrets Act of 1911* but could be if the Sec of State so designated. It would be unlikely except in times of war or other grave international situation. Taking pictures at or in the vicinity of prohibited places (typically military establishments but also including such places as some of the UK Automatic Energy Authority sites) could lead to very serious criminal charges.
(* everyone is subject to the law including the Official Secrets Act and ignorance is no excuse so the phrase we often hear about 'signing the Official Secrets Act' is not a strict requirement, though certain government employees and others often do have to sign a declaration so that their attention is specifically drawn to the Act)
UK airports are all owned by someone and, in the same way that I could tell someone not to take photographs inside my house, so can airport owners tell people not to take photographs inside their airport.
If a person refused to stop taking photographs they could be asked to leave the premises and, if they refused, could be ejected as a trespasser using only the minimum of force required to achieve the object - this is done under civil law and not criminal.
Some people will claim that their privacy has been invaded or their copyright breached when someone takes a picture of them even if in a crowd scene. Human rights and data protection are also brought up at times. Generally, none of these apply but there could be specific circumstances when they might.
Another thing that ought to be born in mind is photographing children. I'd be very careful to ensure that any children not in my group were not obviously part of the photograph. Tv companies often fuzz children's faces in crowd scenes on the news programmes for example.
In this country we seem to have gone way over the top in the name of such things as data protection, child protection, security and health and safety but it's best to be aware of the possible pitfalls especially if an over zealous airport official decides to exercise some 'power'.
The best advice is to act reasonably with the camera but if you are challenged by a bona fide airport official or police officer and told to stop you have no option but to comply as you are on airport property.
Airport officials such as security staff have no authority if you are on public property (eg a public road or pavement) photographing the airport although police officers have and could find all sorts of reasons to stop you if they were so minded. Some might not be strictly lawful (they would be using what is known in the trade as the 'Ways and Means Act') but you would have to be sure of your ground to resist.
got stopped in quad cities iowa one. for taking photographs. was told to put camers in bag.out of sight. last time it went through quad cities.people taking photographs. i think it depends a lot what sort a day they have had.but then some people have an attitude problem.
i think before taking pictures is have a look round and see if any one else is taking any.a fair guide with that one.
I have been asked to put my camera away at Edinburgh Airport, but never at Manchester. LBA doesn't offer much in the way of photo opps, and I've only ever filmed at Heathrow once, but again no problems. Abroad I've never had a problem.
Whether it is illegal or not, many airports provide facilities to take pictures, so would have problems trying to enforce it. Most European countries employ "terrorist activities" legislation if they need to prosecute.
As previously said, use your head and assess the situation.
I am quite certain that you are not facing any issues in the UK airports (at least the London ones, where I have taken several photos myself). Certainly, it is best to understand that the ongoing security measures may leave some airport officers very serious about the job their are assigned to do, so maybe one is to avoid snapping the photographs next to check-points so to avoid any questions, but other than that, it is pretty obviuos that many farewells are said at the airports, with the photos being snapped, forbidding of which is very difficult to control.
Simple answer to this one. Most places in the world have aviation enthusiast/photographer groups these days. Many have web pages they keep up to date and they list good photography spots, no go areas and a host of other valuable information. There are also general sites listing photo spots at airports around the world but these tend to be more patchy and less up to date. Another way to find local info is by contacting photograhers contributing to aviation photography sites or Flickr. They will know the does and don'ts for their localities.