First off, certain famous ocean currents have well-known effects on climate. Consider the Gulf Stream. The climate in Northwestern Europe (the UK especially) is much more mild than it is directly across the Atlantic in Canada and the Northeastern US. There can be up to a 30-40 degree (Fahrenheit) air temperature difference in January between these two areas. The Atlantic Ocean near Canada is locked in ice in winter but the Atlantic Ocean near England is not. It is thought that the huge temperature difference is due to the Gulf Stream, one of the strongest currents in the ocean, and one of the best studied. (Ben Franklin was one of the first people to map this current. You can check out information on Gulf stream History.)

The Gulf Stream brings warm water from the Carribean and Florida north, along the coast of the US, and then east across the Atlantic to Europe. Because it takes a right-hand turn somewhere around North Carolina, the warming effect of its waters misses the Northeast US and Canada, but does reach England and Ireland. Take a look at some maps of the The Gulf stream and maps.

Wheither or not you think that the relatively mild climate in England, Scotland, Wales, Ireland and Northern Ireland is due to the direct effect of the warm water in the Gulf Stream, or to the indirect effect of The Great Ocean Conveyor Belt ("thermohaline circulation"), of which the Gulf Stream is a part, either way the warming is partly caused by ocean currents. If the Gulf stream was to slow down considerably (as it has in the past), then winters in Europe would become very cold. The last time this happened, from 1450-1900, it was called The Little Ice Age.

There is some concern that current global warming caused by rising carbon dioxide concentrations will cause the polar ice cap to melt and slow down the Great Ocean Conveyor Belt, thus slowing down the Gulf Stream and sparking a cooling event in Western Europe. This is the (tiny bit of) science behind the movie "The Day After Tomorrow". Many scientists think this is unlikely, but recent research shown that past ice ages have been linked to slow downs in the Great Ocean Conveyor Belt. Check out Abrupt Climate Change.

The Gulf Stream is just one example of how ocean circulation affects climate. It is a more complicated story. Winds are an important force driving ocean currents. Winds, in turn, are partly driven by differences in heat from one part of the globe to the next. As global warming affects the global heat budget, it will alter the strength and direction of winds, which will alter the strength and direction of the major ocean currents. We already see evidence for changes in ocean circulation due to global warming, but I don't think anyone knows enough about the complex interaction of winds, currents and the global heat balance to predict what will happen as more and more warming occurs. As ocean currents change (and they will), not only will climate change, but marine ecosystems will change as well, with potentially dramatic effects on all ocean life, as well as on the human food supply. (More than 1 billion people rely on fish as their primary source of protein.)

The contribution of the ocean currents to the climate exists, and it also works in the opposite direction. I mean, the climate also contributes to ocean currents. Ocean waters are constantly on the move. How they move influences climate and living conditions for plants and animals, even on land.
Currents flow in complex patterns affected by wind, the water's salinity and heat content, bottom topography, and the earth's rotation. Surface water movement takes place in the form of currents. Currents move ocean water horizontally at the ocean's surface. Surface currents are driven mainly by the wind. Other forces such as the Coriolis effect and the location of landmasses do affect surface current patterns. The Coriolis Effect explains how the earth's spin causes the wind to curve. The wind in the northern hemisphere curves to the right and the wind in the southern hemisphere curves to the left.
In fact, huge circular patterns called current gyres can be seen when looking at the world's ocean currents. From the equator to middle latitudes, the circular motion is clockwise in the Northern Hemisphere and counterclockwise in the Southern hemisphere. Near the poles of the Earth, there is a tendency for the gyres to flow in the opposite direction. This circulation of water helps spread energy from the Sun. The Sun warms water at the equator and then water and heat are transported to higher latitudes.
An example is El Nino. El Nino is a name given to the occasional development of warm ocean surface waters along the coast of Ecuador and Peru. In El Nino years, the Equatorial counter current intensifies in the Pacific Ocean.This current flows towards the east, and it is a partial return of water carried westward by the North and South Equatorial currents. The effect of El Nino brings changes of weather raising or lowering air temperature, and amounts of rain. These factors contribute to change the weather in different places and in different forms.

Currents flow in complex patterns affected by wind, the water's salinity and heat content, bottom topography, and the earth's rotation. Upwelling brings cold, nutrient-rich water from the depths up to the surface. The earth's rotation and strong seasonal winds push surface water away from some western coasts, so water rises on the western edges of continents to replace it, which is why the ocean is so much colder on the east coast than the west coast. Marine life thrives in these nutrient-rich waters. Colder or saltier water tends to sink, so you can imagine that the waters off the coast of Antarctica are really cold. A global "conveyor belt" sets in motion when deep water forms in the North Atlantic, sinks, moves south, and circulates around Antarctica, and then moves northward to the Indian, Pacific, and Atlantic basins. It can take a thousand years for water from the North Atlantic to find its way into the North Pacific.
Oceans store a large amount of heat, so small changes in ocean currents can have a large effect on coastal and global climate as they carry enormous amounts of heat north and south.

Ocean currents move warm and cold bodies of water around. Water has a specific heat capacity thousands of times that of air, and as a result are able to chill or heat the air over them, as well, as are the source of vapor that becomes clouds and precipitation.Simply enough, the Earth's air-flow patterns are atmospheric, but the air temperature and even moreso the precipitation depends on ocean currents.

Oceans play a HUGE role in redistributing heat around the globe. Ocean surface water that is heated by the sun near the equator eventually makes its way to the high latitudes where it cools off. When it is cooled, it sinks. Eventually, that cooled water makes its way back to the equator where it wells up and becomes surface water again. The whole cycle then repeats itself. This system of upwelling, heating, cooling, and downwelling is called the global thermohaline circulation system. Itsprimary influence is to transfer heat from the equator to the highlatitudes. One fear related to global warming is that rapidly melting polar ice sheets could cause this circulation system to cease. Melting of ice sheets delivers huge influxes of fresh water to the polar oceans. Because freshwater is less dense than sea water, it sits on the surface of the oceans and prevents the sinking that is necessary to drive the circulation system. The effect of this is that the higher latitudes (England, for example) would become much colder because no warm surface water would be brought to the poles and the lower latitudes (around the equator) would become warmer because there would be no upwelling of cold water.