The ocean currents are the movement of the ocean waters, with the warm ones moving toward the higher latitudes, and the cold ones moving toward the lower latitudes. In order for the ocean currents to entirely stop, all the water in the oceans should have the same temperature, thus its density will be the same because of it, so there will be no movement in the manner as the ocean currents do. This is highly unlikely to happen though, as this will require all the water to be at the approximately same latitude, as well as to have the same depth, thus to have the same temperature and salinity, and because of it, the same density.