Depends on where you're traveling. Most places you'd go as a 'tourist' are generally safe enough - not to say crime doesn't happen and cameras might get stolen every once in a while, but play the odds - how many thousands of people go through a place like Barcelona or Milan and don't have anything stolen, versus the handful that do? Most places in Europe & Asia, as well as the Caribbean, that have anything to worry about as far as theft, are usually pickpockets - so you have to be a little more aware of backpacks/bags, and wallets in pockets, than you do about a camera around your neck. Sling bags can be good because you can keep them under an arm...make sure openings into the bag are in front of you rather than behind...and always keep flaps/zippers closed. One extra safety touch can be to use bags/packs with velcro, or even adding velcro to a bag's lid - it's noisy and sticky when it opens and can alert you to someone attempting to sneak in. Usually these are not violent offenders, and will run off if they think they're being caught.
Now if you're going to a seedier location, some third world countries, there is a higher risk of some grab-and-go, knock down, or even hold-up type thefts. They typically won't target someone who looks very aware, takes precautions, and doesn't have too much 'temptation'. In these cases, I'll often leave the camera bag in the room, and just pick one good walkaround lens to mount on the camera. I generally avoid putting it around my neck - opting instead to hold it always in my hand, with the neck strap wrapped firmly around my wrist...I keep the camera in front of me most of the time. There are tricks to make your camera look less desirable - cover up the brand name on front, add some gaffer tape around the grip, focus ring, or battery door to make it look 'broken' and used...just little things to make it look like your camera isn't a top of the line DSLR and not worth taking. Avoid jewelry, nice watches, etc. Keep credit card or money in a front pocket rather than back, leave the purse/bags if you don't need them. I've walked around some seriously gritty places with my DSLR, taking plenty of photos, with no problems just by using these logical precautions. Some Caribbean islands, some towns in Brazil, some eastern-European countries, and some spots in Africa might be places you should consider these types of precautions.