Update: I've posted an updated version of this here: Hiking with a DSLR Part 2.
I just spent a week in Rocky Mountain National Park hiking with my family. It was a great week, and it allowed me to give my new hiking setup a full workout.
My camera is a Nikon D300, and my primary hiking lens is the Nikkor 17-55 2.8. Since I have small kids, I carry a child carrier, either a Kelty FC3 or FC1. None of my normal carrying solutions (outlined below) worked for hiking, so I needed something different.
I came across the Cotton Carrier, which is a chest harness for the camera. You screw a small round attachment into the bottom of your camera, and it slides into the chest harness. It also provides a Velcro strap to immobilize the camera further, although I only use this if I need to scramble up rocks or jog. It also provides a safety strap that I attach to where a normal camera strap would attach.
In this setup, I don't use a camera strap at all. Between the harness and the safety strap, the camera isn't going anywhere, and it provides for clean access to the camera.
When I first got my carrier, it didn't come with the safety strap, and I kept a very short camera strap on the camera to provide for a little extra safety when I had it out of the carrier. When they added this feature they offered it for free (plus postage) which was a nice touch.
This setup worked pretty well, but it was frustrating to use the Tripod which I sometimes carry with me on hikes. To address this, I moved to a solution where I 'always' used a quick-release solution.
I use Arca Swiss compatible plates and clamps. Initially, I had a generic plate for my D300 and a Kirk QRC-2 clamp on my tripod. This worked alright, but the plate was bulky so I always took it off the camera when I wasn't using it, which was time consuming.
I looked into using quick release plates with my Cotton Carrier and realized all I needed was an additional clamp. You simply screw the Cotton Carrier round attachment to the Clamp, and then you simply clamp the clamp to the camera. This approach increases the distance from the camera to the carrier a little, but I didn't find it to be a problem.
I also upgraded my generic plate to a Kirk plate made specifically for the D300, the Kirk PZ-122. This plate was MUCH better than the generic plate I used before. It is much more low profile, and has a 'stopper' you can put on one side to the plates can only go on and off on one side. Additionally, it has a second screw hole, so you can attach the camera to other things that use this attachment without removing the plate. Since I regularly use a Rapid Strap, that screws into that hole, it turned out to be a great feature.
All in all, I'm very happy with the Cotton Carrier + Kirk Plates/Clamp system in general, and for Hiking in particular.
The harness looks like it covers your entire chest, but only the bottom band (about 1 1/2 inches) is really snug against your chest. It does get a little sweaty, but not bad considering, and nothing compared to my hiking backpack.
When I'm not hiking, I use one of the following (all of which I like for specific uses):
The R Strap works great when you are shooting a lot with the same lens and a 'casual' level of movement. It is not good for walking on non-level ground, walking long distances, or doing a lot of squatting.
I rarely use the camera with a normal camera strap, but it is the traditional approach.