Having said all of that, many museums do allow you to take photographs, but that doesn't give you cart blanch. You still have to be respectful of the fact that you've been given permission. Even if you've got great equipment, and you're an almost professional, chances are you're not. I don't want to burst your bubble, but unless the museum invites you to come take pictures, you have no additional rights or privileges than the hundreds of other people coming to see the exhibits, no matter how cool your gear is. I've been lucky enough to shoot for an archaeological dig, and I was shooting very rare pieces, and there are several differences between you visiting a museum thinking you'll get professional shots off, and being a professional.
These differences are also why you'll never (or at the very least rarely) ever get a perfect shot of any item at a museum. The first thing that professionals get that you will almost never get, is good lighting. The lighting in a museum is designed to tell the story of the exhibit. Shadows are cast for drama, lights are set up not only to see the item, but also to read nearby plaques. The lighting set up for most museums is often great for shooting whole rooms, but often horrible for shooting a particular item. Museum designers design these rooms for the pleasure of the guest that wants to see these items and learn something, not for any photographers.
The other problem you'll often come across is glass (or Plexiglas). Many museums keep their items behind glass, this is to keep the items from being touched, as well as in some cases keeping their environment perfect. Glass creates reflection, as well as changes colours and light. When shooting professionally the first thing any museum will do is get rid of the glass.
The final problem you'll come across is angles. Museums do their best to show off items from the best angle, but they have limitation. They have space limitation, security limitation, and sometimes physical limitations. This can truly limit how you shoot anything, and most importantly will limit how the light reflects off of the item. In a professional situation you're able to move the item any way you need to get the proper shot. You're also able to use various photography tools to hold up the object for maximum angle benefits.
I have two pet peeves with photographers in museums. I've seen people with the best gear and people with simple point and shoot cameras both offending hundreds of times. The first is the slow picture taker. I've seen people standing right in front of famous museum pieces taking forever, while other people wait patiently. I find that this is a result of one of three things. It could be that this person is trying to set up the perfect photograph, if you've read anything I wrote above you'll know that the odds are stacked against you. Just take a quick picture, and move on, if it's out of focus or lit poorly it's probably not going to get any better. I assure you it's not your fault, it's the display.
The second pet peeve I have with photographers in museums is anybody using a flash. Keep in mind I don't blame anybody who accidental sets off a flash, it happens. I'm talking about those who purposefully use flashes in museums. First and foremost, most museums do not allow flash photography. The official statement on this is that flash photography can often damage the object you're trying to photograph. While I'm sure this rule is exaggerated, since a piece of stone that's been out in the sun for thousands of years will probably not be damaged by a flash, it seems to be a good deterrent for flash photographers. The reason I hate flash photographers most is the fact that they're ruining everybody else's time at the museum. I can't tell you how many times I've been blinded by some idiot with a flash at a museum. Also, if there's glass between you and your subject, there's a good chance the pictures not going to work. So put away the flash already.
The reasons that "make sense" to me are as follows: Academia has a rule about archaeological items found on sites. No photos of these items are allowed to enter the public domain until they have been published in a scholarly journal. I'm not really sure why this is, in fact I think it's rather silly, but since they did all the work of digging these things up, you might as well respect the rule. When one particular item has been blocked from being photographed, this can be the reason. The problem is that many scholars can be really slow at publishing their work (we're talking 5 or 10 years in some cases).
Another reason that you may not be allowed to take pictures is security/safety of the item. If an item is very valuable they may ban photography because this gives the people that might want to steal it an opportunity to photograph the security features of the walls and case it might be stored in. In other cases it could be to make sure that the item is not damaged. Now you may be asking yourself, how do you damage anything by taking a picture, the answer is, you can't. However, you can damage an item by using a flash, and if you'll read above, some people that use flashes at museums are inconsiderate jerks, and don't care about anything except trying to take a good picture.
There are two other reason's why you can't take pictures that to me are the worst reasons you can't take pictures. One is that the items might be on loan from a private collector, and that private collector is an ass that doesn't want you taking a picture of his/her thing because it belongs to them. While this is a truly asshole thing to do, it is their right. The second reason you may not be allowed to take pictures is because the museum wants to sell books and postcards. While I think buying a postcard or book with photos of an item you're really excited about seeing is a great idea, I think banning photography for this reason is a horrible thing to do. While I've never talked to anybody at a museum who has admitted this, I'm certain it can be the case.
Later