Let me start by saying I prefer not using a strap at all.
I know this is personal preference and is related to shooting habit, but what are the general pros and cons for using the strap that came with the camera (and not other specialty straps).
Also, what other straps are available? How do they address the problems of the default strap?
Context is what defines what a photographer should use. Without knowing in what context people use camera straps, it's tough to pick if a strap is right for you, and if so, which.
The strap I use is a heavily padded version of the standard neck-strap. It makes a world of difference for comfort but otherwise works much like standard strap. Actually, it has a quick-release system which I rarely use.
PROS
Faster lens changes: Straps allow a camera to hang conveniently right in front of me -- a great spot to change lenses, which I sometimes do dozens of times per day. When strapless it takes me at least twice the time.
Fail-Safe: The neck-strap I use stays on my neck most of the time. If I set up my tripod on a precarious location, I keep my neck through the strap. Shooting downwards from a balcony, you better keep the strap on!
Security: Keeps the camera safe from accidental knocks. If it gets knocked or I get pushed, chances are the camera will not fall. In some environments such as crowded streets or markets, it is impossible to prevent something from knocking the camera.
Hands-Free: There are plenty of things to do while taking pictures that work better with both hands free: handing out business cards, writing people's emails, handing model-releases, etc.
Anti-Theft: There less risk someone can take away my camera if its attached to my neck. Some camera straps have en embedded metal wire to prevent slashing.
Multiple Cameras: The straps may get entangled but at least it makes it easy to shoot with multiple cameras.
CONS
Noticeable: A camera strap makes it obvious that there is someone with a camera taking photos.
Shooting Down: When shooting the nadir shot for a panorama, the strap needs to be carefully folded up to prevent it from showing up in images.
ALTERNATIVES
There are a few different straps which I use regularly, mostly with smaller cameras. My favorite stealth strap is a Hand-Strap, which wrapes around the palm, though some photographers prefer a wrist strap. Pros/Cons for these straps:
More safety than no strap. Particularly from accidental knocks.
Strain risk: With a hand strap you support the weight of the camera at all times, so I rarely use it with something big.
There are tons of custom straps and I have had issues with all of those that I've tried (I haven't tried them all) except for the Bosstrap:
Block the tripod mount: Most rapid straps hook to the tripod mount which can be annoying when using a tripod.
Poor tripod contact: Even the few models with a pass-through offset the mount making it so your camera is no longer aligned on its optical axis. Straps can also reduce the contact-surface between the camera and quick-release plate.
Where is the bag?: Have you seen the videos selling rapid straps? People never use a camera bag! My guess is that it would get entangled with a shoulder-bag (my favorite) and not work at all with a sling (second favorite) and probably cause difficulty with a backpack, which you should probably never use for photography anyway.
There are a few more complex options aimed at professionals that I haven't yet tried:
Harness: Good comfort and distribution of weight. Holds multiple cameras easily. Extremely secure.
Holdster: You can have holders which attach to your belt (actually, a friend had two sown to a padded belt) and simply draw the cameras out and drop them back when you need to free your hands. This worked well for 2 cameras with one lenses each but probably wont scale.
Belt-Clips: At a local store I saw a clip that attaches to an ordinary belt with a matching piece that screws into the tripod-mount (not my thing) but lets the camera slip and lock into the clip quickly.
You can free both hands even when you have no surface to rest the camera on. I don't babysit my camera and I put my camera on the ground as long as it is dry, but putting it on the ground would not be an option when its muddy/wet, or is covered in wet grass etc.
People knows that you are a photographer. Obviously not good for candid shots, but in a wedding people immediately recognize your role and that can be a good thing.
You don't drop your camera when it slips out of your hand.
Ergonomics perhaps? This might be more true when you are using a small lens. When you have a huge lens mounted however, I doubt if your neck should be doing all the lifting.
Some people use it as a stabilizer. There are a few ways to do this, actually. Some wrap around the wrist, some have the strap pulled tight against the upper arm (triceps). It can be used creatively as a mean to stabilize the camera a bit more.
The strap is a great for lens change, especially when you cannot rest your camera body somewhere.
I had actually dropped my camera once because I had a strap. Call me an idiot, but I actually released my hand believing that the camera was strapped to my neck only to find out that I took the strap off my neck earlier because of how frequently it got in the way. I have learned the hard way to not rely on a strap after that. I have also dropped my camera because something caught the strap and yanked it down from my table.
People notice you. Seriously, a strap is designed to be noticed, if you wear it you are bound to be noticed like the people noticing the bastard who didn't turn off his cellphone in the cinema. With a strap dangling around, it is also hard to conceal your camera unless you fold the strap into a ball.
It gets in the way of shooting a lot. If I am using a strap, I must take it off my neck before I can shoot from close to the ground, shoot from my hip, shoot high above my head. The minute you take it off it will block your lens when you are shooting downwards. Using a wide angel lens I sometimes shoot "blind" and the strap get in the way more often than I would have thought.
It puts strain on your neck especially when having a heavy lens mounted.
The length is never right. The more you shorten it the more you want to take it off because of the limited reach and how uncomfortable it is. The more you lengthen it the more you swing your camera around banging it into a table or other things. It also becomes easier to slip off your shoulder and block the lens when shooting downwards.
You must fold/tuck it in every time you put it in a camera bag. You must also unwind, untangle and flip it so it is not twisted every time you put it on your neck.
For me, the cons simply out-weight the pros. I rarely use a strap. Occasionally I would decide to use a strap because of some of the pros I mentioned above, however I usually end up removing it minutes after I started shooting because of the exact problems I listed.
I am not familiar with other strap systems and frankly I don't have much faith in them. I shall leave this section to people who have tried other strap systems and found something that they enjoy using.
It gets in the way of shooting a lot; The length is never right -- You're using the wrong strap!
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Most of your negative points stem from having the camera strap around your neck. What I do is wrap the strap several times around my wrist and already a lot of your negatives dissapear:
because the strap is wrapped so tightly around your wrist, the camera will drop only a few centimetres if you accidentally drop/release it
The strap doesn't attract much attention any more
A drawback of this method is that you are almost forced to walk around with your camera in your hand because it is cumbersome and time-consuming to unwrap.
Also, part of the strap can obscure the viewfinder while shooting.
If your camera is not very heavy, I highly recommend a 'hand strap', like this. I use it on my 20D and 5D Mk2 with all but the heaviest of lenses. It makes a great carrying handle as well when I'm not shooting.
In addition to camera bags designed as a "holster" such as the Naneu C5, there are systems such as the Capture Clip, and the Spider Holster which allow you a little more versatility.
The Capture is pretty nice because the mounting plate is Arca Swiss (you have to use their plate with their bracket, but their plate works with other Arca Swiss things, like tripod heads), and it has a fairly low profile. I have medium sized hands and I can use my camera in portrait mode with my hand wrapped around the grip and over the bracket without any issues. It's not uncomfortable like other brackets I've tried. The only disadvantage I can think of is that the bracket can be uncomfortable if you're sitting down and it's around your waist.
The Spider Holster comes highly recommended from some pros I know. At $135+, the Spider is relatively expensive, but it is supposed to be very comfortable and secure.
As an alternative strap I'd recommend the Pacsafe Carrysafe. It contains thin metal wires that protect the camera from getting ripped by a cutter knife.
The strap is much more inconspicuous then the original yellow Nikon straps. On the downside, a pickpocket could become angry about a failed theft...
I usually carry my camera over neck and shoulder, somtimes like BioGeek. The length allows me to get free from the strap very fast.
I use a BlackRapid RS-Sport strap. One of the best purchases I made. Stops the camera from hanging around your neck and is really easy to shoot with while keeping the camera secure.
Works great for pros or just amateurs carrying around a camera around all day on vacation. I've walked up mountains with this thing and it never gets uncomfortable or in the way and easy to get to when you want to take a shot.
Cons: I've seen several cameras crash to the floor after being accidentally dragged off some horizontal surface by their strap.
What I do to every camera I get is to put a small loop of strong nylon cord through the eye. I carefully size it so my first two fingers fit through snugly. Now, I can work my fingers through the right loop and the camera is more or less attached to my hand.
You can still attach a strap to the nylon loops, but unlike the metal split rings that are often there, the nylon won't scratch up the camera body.
Some cameras have flat strap eyes. You can use nylon webbing in such cases.
I would use the Black Rapid Tether kit on the D800 for additional safety
