Some people actually sling it over one shoulder, only to see the camera crash to the floor when one is momentarily distracted. I find the traditional camera strap very useful when I wrap it around my hands when shooting, but never for carrying the camera around hands-free.
There are a couple of different variant designs on the camera strap in the past years, and two of the most interesting ones are the Y-Strap and R-Strap. Both straps run diagonally down your body supported by one shoulder, and the camera rests on the opposite hip. The weight is on the shoulder and not on the neck, which makes for comfortable wear for longer periods. The camera slides up smoothly along the strap to your face, guided by the length of the strap.
So if you're not happy with the traditional camera strap and want an alternative option, check out the Y-strap and the R-Strap. I like the fact that you're not advertising a huge DSLR on your chest that screams "I'm a photographer!', which means you can probably get closer to your subject without them noticing. Just watch out when you walk past tables - you definitely don't want your precious lens or camera meeting the corner of some sturdy benches!