The wearing of the green - the green is symbolizing the shamrock which is what St. Patrick used to symbolize the Holy Trinity.
Parades - the first parade was celebrated in New York in 1909 after 1 Million Irish people immigrated to the U.S. Countries around the world have parades for St. Patrick.
Greening of monuments - In 1962 Chicago put 100Ibs of green dye into the Chicago river and turned the river green. Other monuments that get turned green are the White House, Disney Land, Leaning Tower of Pisa, and the Pyramids of Giza