If you have an expensive DSLR camera, get a hard case for it, that will protect it from being damaged in transit in most cases. You will also need a shoulder bag for carrying it around during the day. If you are flying, try to make sure you keep your camera in your carry on luggage.
Avoid temperature extremes as well. If you are driving, don’t leave the camera inside the car on a hot day. Put it in the trunk if you don’t want to take it inside where you are going.
If you have a point and shoot camera, you don’t need to be as careful. It is still a good idea to avoid temperature extremes, and having a good case for that is important too.
Carry a few photo cards with you. These cards can wear out, and sometimes your photos are priceless to you anyway. It is a good idea to shoot on a few cards throughout the day. Download your photos each evening and start fresh with your cards each day. This is mostly just to keep from losing photos, and to minimize loss if something bad were to happen.
The next biggest area of concern is security. Depending on where you are going, it could be very dangerous. There are thieves just looking for an opportunity to steal a camera, and there are professionals looking for someone who is being careless. Watch your surroundings and follow your instincts. Some areas are very safe and some are not. In many areas just being a little watchful is all you need to do.
Carry your camera in a shoulder bag. A backpack can be opened from behind you and items taken out without you even realizing it.
There are times though, when you might venture into a bad part of town, or an area where there is criminal activity. For times like these, tape over the brand name of your camera with black tape.
If you use a Nikon, for instance, black out that word, so a would-be thief will not know the brand he or she sees. It may not stop someone, but someone looking for high value for quick sale might pass on a plain looking camera if they don’t know what kind it is. You will need to do the same to lens caps, and get rid of the shoulder straps that came from the company, which gives away the brand name as well.
If you are in a crowded area, or an area where you think there might be a problem, try to keep your camera out of sight as much as possible. Keep it in your bag and out of sight until you are ready to use the camera. It is a little more hassle, but this way you are not inviting attention to the camera.
Another piece of advice is, if you are just shooting snapshots and are concerned about safety at all, it might be a good idea to leave the DSLR at home. Get a point and shoot type camera. These are relatively inexpensive, and fit easily in your pocket. Thieves rarely prey on these type of cameras. You wont have all the creative control you might like, and quality may suffer a bit, but your equipment will be safe.
Also be careful about being around water with your DSLR. It has sensitive electronics and if it gets wet you may have a lot of trouble. Even if some manufacturers claim their camera is waterproof, if it is not specifically made for underwater photography, avoid getting it wet at all costs. Even a point and shoot can be ruined if it is dropped in water or gets rained on.
If you are traveling the countryside in your own car, it is probably safe enough to carry the more expensive DSLR equipment. Make sure your lenses are properly stored in your bag, and only bring along what you think you will need. You can get a smaller bag too, to carry just the camera and leave all the other stuff in the car while you travel. Just don’t leave the camera in the car where it can be seen. Avoid leaving a camera in a car on a hot day as well. Extreme heat can damage the sensors in a digital camera.
A final precaution is to make sure your equipment is insured when you travel. You need not do this if you have a point and shoot, but expensive DSLR equipment costs a lot to replace, so it is wise to have insurance on it, traveling or not. Some homeowners policies, and even car insurance policies, cover theft. It is a good idea to make sure they cover theft anyway. You can always get a small policy to cover theft or damage while traveling, and those are fairly inexpensive.
Make sure you have a cleaning kit and a can of compressed air. You will need to clean the camera every day. Usually just spraying the pressurized air on it takes are of any dust that has gathered during the day of travel and shooting. Clean your lenses as well, and again try to just use the air.
While you take all these safety precautions, don’t forget to have fun with your camera, which is why you got it in the first place. Experiment with your picture taking. Try angles and perspectives you have never tried before. Take a lot of pictures of everything you shoot.
Take the usual shot, and then try it another way to see what happens. While traveling you have time to play with your equipment, so see what it will do. Experiment with the settings. See how creative you can be with your camera. You can always delete what doesn’t work.