Worcestershire sauce does not need to be refrigerated once the bottle has been opened, as there is nothing that can spoil in the condiment. There is a school of thought that Worcestershire sauce should be refrigerated if it is used infrequently, but this does not add to its shelf life.
An unopened bottle of Worcestershire sauce will last indefinitely while an opened bottle of Worcestershire sauce will be good for up to 4 years. However, even after that time, the sauce does not go bad. What occurs is that flavors begin to mute and do not serve as well as an ingredient after that time. For best storage, keep the bottle of Worcestershire sauce in a cool dry place, such as in a food pantry. As with many prepared foods, the bottle should avoid temperature fluctuations or direct sunlight.