What major astronomical discoveries have happened in the last 100 years?

Wow...That's a great question, and a lengthy one to itemize, but let me take a crack at it!

1865  Kirchhoff and Huggins use spectroscopy to identify elements in
      distant stars.
1880  Henry Draper make the first photograph of an astronomical object.
1904   Discovery of gas between stars by Johann Hartmann.
1909, 1986  Halley's Comet returns.
1910  Ejnar Hertzsprung and Henry Russell  establish the stellar
            classification scheme based on luminosity and spectral type.
1919  Einstein's Theory of general relativity tested during a solar 
             eclipse.
1920  Harlow Shapley determined the size of the Milky Way.
1926  Lindblad and Oort establish that the Milky Way rotates.
1928  Edwin Hubble discovers that the universe is expanding
1928  Thermonuclear fusion identified as the energy source of the Sun 
       and stars.
1930  Clyde Tombaugh discovers the planet Pluto.
1951  Emission from hydrogen gas in interstellar space discovered
1964  Quasars are discovered by Alan Sandage.
1965  Arno Penzias and Robert Wilson discover the cosmic fireball 
            radiation left over from the Big Bang.
1967  The first pulsar was discovered by Hewish and Burnell
1968  Water and ammonia gas detected in interstellar clouds
1969  Apollo 11 astronauts set foot on the Moon.
1976  Viking 1 lands on Mars.
1987  The first supernova discovered in modern times is observed.
1904   Discovery of gas between stars by Johann Hartmann