Umami taste can be found in many foods such as walnuts, grapes, broccoli, tomatoes, mushrooms, seaweed and parmesan cheese. But the most common we are familiar of is Monosodium Glutamate (MSG) or Vetsin. It is also in soy sauce, fish sauce and ketchup.
In 1907, Professor Kikunae Ikeda of Tokyo Imperial University started his experiments regarding the taste apart from the 4 common flavors known to man. He knew that umami can be tasted in dashi stock (soup out of kelp which is used as base for many Japanese dishes). Prof. Ikeda extracted glutamic acid (glutamate) from the konbu broth, crystallized it and called it 'umami,' coined from the Japanese word umai (delicious).
(photo and other info courtesy of http://www.glutamate.org/media/discovery_of_glutamate.asp)