Sometimes [with Civ 3 complete, conquests] all my units start moving at a crazy speed. It is as if they were using railroads.
Then I have to close the game down and sometimes even restart my computer to get them back to normal speed.
What causes this?:confused:

You probably have Caps Lock on, which takes away animation from all units. Turn it off and they'll go back to normal. If that doesn't work, check your Preferences (Control + P) to make sure you have animation on.