Farmers and gardeners have long used manure (cattle, chicken, etc.) to replenish depleted humus and fertility in soil. Manure is not a good idea unless you don't mind pulling weeds (and you will exponentially increase your weeds wherever you put the manure). But heavy application of mulch (6 to 8 inches) such as alfalfa hay (which is bailed before it goes to seed) will all but eliminate your weeds from use of readily available manure.
Offered by Roger.
In bigger gardens, you can beat the weeds in an organic way, by laying out black woven plastic mats. This way the weed doesn't get the change of coming up. The mats have to be woven, because if you just lay out plastic, the soil can't breath and will go to rot.
Offered by Jeroen.