As of May 2015, the digital camera with the shortest shutter lag is the Nikon D2Hs, with a speed of 0.037 seconds. However, shutter lag is not the only feature that determines how long a camera takes to react to a press of the shutter button before taking a photo.
On most digital cameras, pressing the button activates the autofocus feature, and the camera begins moving the lens back and forth trying to find the ideal focal length. Once the camera focuses, it triggers the shutter. Turning off autofocus on any digital camera significantly reduces the total lag between pressing the button and activating the shutter.