Quote: "Actually they don't... Most online games calculate the movement both on the client and the server, but only the key-presses are sent to the server, so the client calculation is just to make it feel more responsive. Calculating 3D movement is not particularly processor intensive either."
You have, unfortunately, contradicted yourself. Also, if the server calculates movement of every player, games like World of Warcraft, which has 3000+ players per server, would be unbearably laggy.
And, collision has nothing to do with the server as all the world data is on the client, else it would be ridiculously complex.
Hope this helps.
-Mike