Until recently I have used a wide neoprene type strap on my camera, where it attaches to the normal fixing loops on either side of the camera. My preferred method of carry is either over one shoulder, or else diagonally across the chest, which worked very well whilst I was using a relatively light camera, but when I switched to a much heavier camera/lens combo I found the extra weight meant the camera strap did not slide well when lifting the camera up to eye level.
The Black Rapid overcomes this problem brilliantly. The fixing point for the camera is via the tripod mount, where a small but heavy duty ring is screwed, this is then attached to the strap by means of a lockable shackle that slides along the strap via a rotating swivel and metal loop. There are also two plastic quick release buffers that slide along the strap, the rear buffer stops the camera drifting too far behind you, whereas the front buffer can quickly positioned low on the strap to steady the camera when not in use.
The carry position for the Black Rapid is from one shoulder to the opposite hip, which may take some getting used to for some, as the camera sits a little lower than it would on a "static" strap. However this does mean that the camera can be worn inside an open coat/jacket where it is quite unobtrusive, then quickly and smoothly swung up into position for a quick shot. Also because of the swivel attachment, taking photographs in portrait orientation is just as easy as in landscape orientation. I found with static straps that they are fine when the camera is horizontal, but if you try turning it on it's side the camera strap would tighten, making positioning difficult, or else there would be loose bits of strap trying to fall over the view finder. Neither is a problem for the Black Rapid.
There are two possible disadvantages to the Black Rapid. The first is that because it sits comfortably low on the hip, it is easy to forget the camera is there, and so it could be more prone to knocks if you try brushing past something. To get over this I tend to walk with my hand resting over the camera (whether it is being worn over or under my jacket), and I always have the lens hood on. The second problem is that because the Black Rapid uses the tripod mounting point, the strap's attaching ring has to be unscrewed from the camera before it can be screwed onto the tripod head / quick release plate. Black Rapid have produced an alternative mounting ring that can be combined with a Manfrotto quick release plate for quick transfer from strap to tripod head, however the first batch of these alternative rings have suffered from quality control issues (tolerances less than 1mm). Black Rapid are reporting that a re-engineered alternative should be available early 2011. NOTE - This only applies to the additional ring for quick release plates, the standard Black Rapid fixing ring is perfectly fine.
If you are prepared to put up with the extra couple of seconds needed to transfer your camera from strap to tripod, then this carry option is brilliant, especially if you are using a heavier camera. Unobtrusive, comfortable to wear and very fast/smooth to use.