How has symbolism influenced the modern world?
As an art form and the means of transmitting philosophical statements, Symbolism is greatly influential in culture. There are literally thousands of conscious and unconscious symbols used every day by everyone in the world; our knowledge of these symbols and their origins is limited only by our desire to understand where and why they originated.
For example, many of the symbols used in the Government of the United States are descended from Masonic symbolism. The pyramid and all-seeing eye on paper money is a good example; nowhere in the mythology of the United States is there a pyramid, nor the eye other than that of God. In fact, the pyramid is meant to symbolize power and strength, as stated explicitly by Charles Thomson, the designer.
In literature, the most prominent theorist of symbolism was Joseph Campbell, who codified the Heroic Monomyth as an archetype and described many of the conventions used in literature and religious mythology. Campbell's "Hero with a Thousand Faces" is the most common sort of storied protagonist, although recent trends have damaged the pure heroism of Campbell's theories. This sort of symbolism bleeds over into real life as citizens have been trained from an early age to expect their leaders to be flawless and selfless in their public works; reality always disappoints, however.
Finally, a good example of symbolism in the modern world is the pervasive nature of Trademarks, the insignias that instantly identify people, places, and things. Since the insignia is intended to fully represent its owner -- the "Golden Arches" means MacDonald's, the "Swoosh" means Nike -- we are trained to recognize all the important aspects of the owner in the identifying mark. The trademarked insignia becomes visual shorthand for the product or service, and those trademarks are stridently defended to avoid a bad reputation.