Conservation: One of the oldest arguments against photography in museums, galleries and country houses is that flash photography can damage exhibits. I'm not an expert but its easy to understand that exposure to light can be damaging to delicate paper, textiles, pigments and inks. While I understand the arguments for protecting such items from the harmful impact of UV in sunlight I don't understand how flash photography can be treated as equally dangerous. Of course most modern cameras are now more than capable of capturing good images in extremely low light so a simple ban on the use of flash would both protect delicate objects and satisfy the needs of photographers.
Perhaps the biggest argument in favour of allowing photography is that pictures are used on a regular basis by conservators restoring old buildings to original condition. Any reputable museum will have a good photographic record of its exhibits but pictures of the context and setting of objects in a country house for example can be vital in successful conservation and restoration projects.
Copyright: Copyright is a sticky issue, particularly for museums that primarily show copyrighted pictures or paintings. But for those museums that are exhibiting historical artifacts copyright just isn't an issue. Besides it's an easy policy to ask that photography is permitted so long as the pictures taken are not used in a way that will infringe copyright (ie for commercial purposes).
Having said that the problem of trying to enforce and police copyright in the 21st century has grown exponentially with the widespread use of digital camera and the Internet. My view is that the only people effected by a ban on photography are those people who play by the rules and would respect issues of copyright. For the less scrupulous (or those with criminal intent) a ban isn't going to stop them without vigorous and intrusive policing by security staff.
Criminals might photograph exhibits so they can be stolen to order or plan elaborate thefts involving laser guided zip-wires and Catherine Zeta Jones in a skin tight bodysuit. And of course a ban on public photography will thwart these master criminals before that have even begun to plan their nefarious crime. Or not. I'm pretty sure that the dedicated museum thief can find ways around a photography ban and once again the only losers are innocent visitors. Similarly I'm guessing that your typical al-Qaeda suicide bomber can probably gain all the information they need for their less than subtle operations from pictures taken in public places not from a closeup of a medieval vase.
Commercial: Museums may fear that pictures taken by visitors will mean they sell fewer reproductions and books in the obligatory shop by the exit. But my experience has been that the sort of museums that operate a ban often don't sell these items so the visitor goes home with nothing anyway. I've been in lots of the big museums in London that have no restrictions in photography but clearly do a big trade in picture postcards, books and reproductions. My personal interest in military museums - in which I have shot tens of thousands of pictures over the years - hasn't stopped me from buying tons of books featuring pictures of the very same objects.
Visitor Numbers: Another popular excuse for imposing a photo ban is that pictures posted online mean fewer visitors through the door. This is one of the sillier arguments against photography in museums. Photographs posted online, on blogs and websites are free advertising not a threat to visitor numbers. I've discovered dozens of little museums this way and later gone on to visit them. I'm sure I'm not alone in this.
One thing I have noticed is that museums that operate a ban often don't advertise the fact on their leaflets or websites. I suspect they don't advertise the ban is because they know that it will discourage some visitors from coming. In other words they acknowledge its an unpopular policy but they are going to impose it non-the-less without even affording the courtesy of explaining their reasons!
The primary purpose of a museum is to exhibit and educate the public about artifacts associated with their given theme or subject. But engagement and education cannot happen if the museum remains a secret known to just a handful of hard core enthusiasts. Either a museum opens its doors fully and welcomes the public or it keeps its doors closed and stays a private collection. If a museum imposes a photography ban "because they don't want to advertise their collection" then one has to ask what is the point of being open at all.
Antisocial Behaviour: Lastly is the often quoted wish to ensure that all visitors can enjoy exhibits equally without photographers getting in the way or disturbing the peace in galleries with beeping cameras. I fully understand why an art gallery for instance might want to ban the use of mobile phones as strident ring-tones can be very intrusive. Similarly flash photography could be disruptive but as I have already said most modern cameras can take pictures without flash. But my objection to this policy stems from the fact that anyone is capable of being an antisocial a**hole irrespective of whether that have a camera on them or not. Banning photography merely targets one group unfairly while letting all the other rude people off the hook.
So what are the options for Museums? One option I am personally in favour of is operating a Permit System. I've encountered this in several museums and public places and it seems to work just fine. The Venue gets to make their photography policies crystal clear and in return for agreeing to them the visitor gets permission to take pictures. A nominal fee could be charged for operating this scheme and so long as it isn't exorbitant I think most enthusiasts would be happy to pay for the 'privilege' of taking pictures. This would help offset any perceived 'losses' in the shop or in higher insurance costs.
For me one of the best arguments for not imposing a Photography Ban is the fact that so few institutions feel the need to impose one. I have visited literally hundreds of museums over the years, from tiny collections run by one person right up to huge national collections. Most that I have been to do not impose a ban on photography and do not seem any worse off for the decision. If they can do it then surely all museums can.