Technically, the terms clockwise and counterclockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is counterclockwise when viewed from the North Pole, and clockwise when viewed from the South Pole.
Clocks traditionally follow this sense of rotation because of the clock's predecessor: the sundial. Clocks were first built in the North Hemisphere, and they were made to work like sundials. In order for the sundial to work (in the North), it must be placed looking Southward. Then, when the Sun moves in the sky (East to South to West), the shadow cast by the sundial moves in the opposite direction, that is West to North to East. That's why hours were drawn in sundials in that manner, and that's why modern clocks have their numbers set in the same way.
Occasionally, clocks whose hands revolve counterclockwise are nowadays sold as a novelty.
Typically, screws and bolts are loosened counterclockwise and tightened clockwise. One mnemonic for remembering this is "righty-tighty, lefty-loosey" (right to tighten, left to loosen.)
In trigonometry, an angle in standard position is measured counterclockwise from the positive x-axis.