Originally Posted by Biffo the Bear:
“You can lock the shutter up on some DSLRs, thus getting rid of the click-clack, but it risks exposing the sensor to more dust etc.”
Also, precise auto-focus usually needs the mirror in place.
A lot of SLRs now have "live-view", meaning the monitor on the back of the camera is used instead of the optical viewfinder. With mine, it locks the mirror up while you compose the shot. Then when you actually shoot, the mirror flips down, it auto-focuses, then it flips back up and opens the shutter, so it ends up being even noisier.
It can be a pain, because it can be noisy enough to scare wildlife, and there can be enough vibration to blur the picture.
There's a growing trend towards cameras with SLR-like sensors, image quality, performance, and flexibility (including interchangeable lenses), but no mirror, and an electronic viewfinder (or no viewfinder, just live-view) instead. Sometimes called EVIL - "Electronic Viewfinder, Interchangeable Lens". These can take pictures quietly. There's much debate about whether they can or should replace proper SLRs.