You don't need to know the settings to appreciate the beauty in the photograph itself. But to understand how the photographer did what they did in the photo, it's essential to know what they did with their camera. It's like asking what kind of stroke technique a painter used in a certain section of their painting. It's just as beautiful either way, but it helps to understand how they got there. Also, knowing the settings can be great when it comes to wanting to imitate the effect in that photo.
Generally, no, but I will confess a certain curiosity when it comes to images that present a technique that I’d like to learn.
On a slightly tangential note, I always list my camera settings and detail any light setups when I post on flickr; I figure the majority of that community is interested in learning the technical details. I don’t, however, reveal my post-processing techniques, simply because it would go over most people’s heads.
Apparently only a few people took the time to look up the definition of "appreciate." If you appreciate something, you don't just like it, you understand it; as in "to appreciate the difference between right and wrong." If you appreciate something, this does not mean that you can, or even should, appreciate it on an entirely visceral level, as some other people here seem to think you should.
Back in the day when we only had film cameras, knowing your settings was essential. Certain light sources needed different settings, depending on how you want the exposure to look with the film you are using. A good photographer could expose certain parts of a shot exactly how they wanted.
Now a days in the digital world, settings are not that important anymore. Everything happens automatically, and you don't have to alter your settings. Take a star filled sky. The correct aperture opening for a star filled sky is 100% open, however you see amazing digital photos taken with F numbers like 22 or 16.
The limitations of film made settings a key factor in professional photographer.
Maybe this is related to the age-old bugbear, "Great image! What camera you got?"! Should make no difference, right? If you think it's good and I tell you it's $20k medium-format or a $50 PnS, would I change your opinion on whether you still think it's great?
Asking for the settings does not equal 'not appreciating it' but rather implies the desire to learn something. Asking about what camera was used is often also very informative. I am sorry, but some photographs can NEVER be achieved using a $50 P&S. If that is all I have and it took you a $20.000 camera to get THAT particular shot I will know that I cannot replicate it. Saying that the camera does not matter for the photograph is utter BS, sorry. Of course you can create stunning photographs with a cheap ass camera, but a full blown DSLR will give you so many more options. A cheap P&S will never be able to take an image like this: (at least not with that detail and clarity) Having a camera/lens combo that does not allow for 2:1 macros will never let you take pictures like this: Having a camera that does not allow doing very rapid shooting will make getting a photo like this very, very difficult: The tools of our trade matter. They do not make us better or worse, but they do limit what we can do. And knowing what was used to get an image will tell me if I can recreate something like it or not.
Without even zooming in on the race car, just looking at the thumbnail, I can appreciate it from an artistic level as a really great action shot. The speed of the machine, the sleek way it's coming around that bend, screams raw power, speed, excellence in engineering a superb capture of a tricky subject. I got all that from that one tiny thumbnail, I sized it up from a purely artistic viewpoint. If I knew exactly what camera, exactly what lens focal length, aperture, ISO, position to the sun, file size, etc would I change my opinions from those above to, "Oh, I see, I don't like now then!", of course not.
My point was, that if something is described by an almost generic comment like "Great image.", me knowing the camera ( and settings ) change my opinion of "Great image." to "Oh OK it's a Canon 1DX with the ultra fast frame rate, oh well it's OK in that case, don't think I really like it anymore to be honest!". Of course not! When I first look an image I make artistic judgements, I take in an image and I make a decision on whether I like it, whether it stirs my soul and appreciation of its content.
When everyone else was going for smaller, newer compact cameras the French master photographer Eugene Atget was was still lugging his huge film plate camera about, his images are no more or less artistic than his compact camera wielding counterparts, they can be appreciated for what they are, great artistic images irrespective of the kit used.
On a purely technical level, dissecting an image and how it was created for educational purposes is completely different exercise. That has a specific goal and you have made a conscious decision to disregard the artistic appreciation for the moment ( or completely ) in favour of the purely technical. Not to say you won't come back to the artistic but that you suspend it in favour of the technical for a period of time.
You only need that information if you're trying to improve your photography and you see an effect that you haven't seen before. Otherwise it isn't going to make any difference. And really, thinking about such things tends to detract from the work.