If the Earth did not rotate, convection currents would move in one straight path, from the equator to the North Pole and back again. The rotation of the Earth causes this path to be skewed so that currents move in smaller circles between these areas. This is called the Coriolis Effect.
The ocean does move in circles. If you look at any map showing ocean currents, you'll see that the majority of them make big, somewhat distorted circles. The continents are in the way, so the ocean currents have a rather complicated circulation pattern (see "Thermohaline Circulation").
There are many things which completely circle the globe. The first thing that comes to mind is the equator, but the artic and Antarctic circles also circle the globe (as well as every other degree of latitude). The taiga forest circles the globe. The atmosphere circles the globe.