Tsunami has been observed and recorded since ancient times, especially in the Mediterranean areas and Japan. The oldest record can be dated back to about 1,700 B.C. A volcanic eruption in Santorini, Greece, generated a tsunami about 100 to 150 meters high, destructing the powerful fleets and the palace of Minoan civilization on the island of Crete, about 45 miles away from Santorini. For more information, see e.g. NGDC tsunami database, History of Minoan Crete, or Important.ca.
People at Hilo, Hawaii, running away from 1946 Aleutian Tsunami (about 2,300 miles away from the source, picture from Wikipedia)
Most of tsunamis occurred in the Pacific Ocean. In Japan, almost 200 tsunamis were recorded in the past 1,300 years. In the past century, several destructive tsunamis occurred in the Pacific, e.g. 1923 Kanto Tsunami (Japan, 12m waves recorded), 1946 Aleutian Tsunami (Alaska, up to 35m runup observed), 1960 Chile Tsunami (up to 10.7m runup recorded at Hilo, Hawaii, about 10,000km away from the source) and 1964 Good Friday Tsunami (Alaska, up to 67m runup measured).
Aftermath of 1960 Chile Tsunami at Hilo, Hawaii (picture from National Geophysical Data Center)
The most deadliest tsunami in the history is probably the 2004 Indian Ocean Tsunami, triggered by an earthquake (Mw=9.3) in Sumatra, Indonesia. Nearly 300,000 people were killed by the tsunami and the earthquake, millions were left homeless.
Vegetations stripped away by 2004 tsunami near Lhoknga, Indonesia (picture from USC Tsunaim Research Center)
The 2004 Tsunami arriving at Ao Nang, Thailand (picture from Wikipedia)