Dunno ... I think that most belief in dowsing is due to a combination of confirmation bias and luck. However, there do seem to be some cases where a particular person seems to have almost uncanny success with the method. From personal experience, I would lean toward the rods (or whatever else is used) acting as a crutch to access the subconscious.
Humans just can't be still. As steady as we think we are, we are constantly moving. Anyone that successfully shoots knows the effect of breathing. Do some long distance shooting with a scope and you can see the effect of the heart. Beyond that, there are micro-tremors caused by minute muscle contractions, of which we are almost entirely unaware. The dowsing rods are constructed so that they are extremely sensitive to movement or tilt. Thus, it would be very easy to cause movement in them without being aware of doing it.
If the unconscious movements of your body are being directed by the subconscious, the rods would seem to move on their own. If the subconscious is using information from prior experience, it could account for accuracy. The fun thing is ... you may be unaware of the information the subconscious is using ... since you may not have consciously noticed it when you received it.
There are no scientifically controlled studies that I know of that have ever shown dowsing to be effective. There have been a few studies that point to the stuff i described above as being how a ouija board works (when people aren't just shoving it around) ... no spirits or magic needed.
My personal experience" is through self hypnosis/relaxation techniques and visualization and I have found pipes and cell phones through it. (and why this thread got my attention). Finding the last cell phone was by remembering my foot hitting something while crawling through attic insulation. The last pipe was a septic line.. after sitting in the middle of the yard and going through my little routine, I opened my eyes and suddenly saw differences in the grass that I hadn't been able to see before... first jab with the probe and bingo!
But... everything I have said may be a result of my own confirmation bias. Science is a process to find truth, not a system of beliefs.