Do all space satellites orbit the earth in the same direction?

The successful launch of the SpaceX rocket Dragon, timed so that the Nasa astronauts onboard could rendezvous with the International Space Station, got me thinking: do all satellites orbit the earth in the same direction? If so, is it clockwise or anticlockwise? Presumably they go in the same direction, or they would crash into each other.

Andrew A, London

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