A number of natural phenomena's can cause tsunamis among these: underwater avalanches, like the Storegga avalanche and the tsunami it caused outside the coast of Norway in 6100BC, meteors and comets striking water, explosive submarine volcanic eruptions and most commonly earthquake tsunamis like the 8.1 earthquake Tsunami of 2009 in American Samoa, the strongest ever recorded 9.6 quake of 1960 tsunami and the 8.8 quake of 2010 tsunami both in Chile, to compare the 2nd strongest quake recorded was at 9.3 of 2004 in Indonesian water, this was the one that caused the great tsunamis of december 2004 which is the most devastating one in modern times.
Underwater and costal avalanche slides
That avalanches could cause major tsunamis is still fairly unknown among most people, this type of tsunami could also be harder to detect since the avalanches could be triggered by minor tremors which then cause the avalanches, this is also why tsunamis could be so dangerous, since the size of a quake does not tell you what it has triggered of small and large underwater avalanches, thus proving this natural phenomena's erratic nature. One of the largest known tsunamis known in fairly recent time is the Storegga avalanche tsunami outside the coast of Norway dated to 6100BC, this tsunami was caused when a submerged landmass the size of Iceland slid into deeper water causing some of the largest tsunami waves in the last 10000 years and it's effect is still found if one know what to look for in the British isles, Ireland, Scotland, Shetland, Iceland, Norway, and Greenland.
Earthquake is by far the most common cause of tsunamis, often the earthquake trigger submarine slides which could cause massive tsunamis even stronger than one expected from the raw Earthquake itself, other times the forces of the Earthquake itself causes minor tsunamis or only very local tsunamis like the quake outside of Chile in 2010, this earthquake even though it was a 8.8 caused massive tsunami waves in Chile but only minor waves across the rest of The Pacific Ocean, like in Hawaii which was put on a tsunami warning, closed down stores, highways and evacuated people from small buildings and in high rises below 4th floor. The 9.5 Chile earthquake of May 22, 1960 on the other hand caused massive damages in Hawaii, wiping out the beach line of Hilo on the island of Hawaii.
Below are some video footage from the tsunami that struck American Samoa after it was struck by a 8.1 earthquake, 29th of September 2009.
American Samoa tsunami footage
Helicopter view of American Samoa tsunami damages
first person footage from American Samoa
Submarine volcanoes and volcanic isles
Another very destructive type of force that cause tsunamis is pyroclastic eruptions of submarine volcanoes, usually submarine volcanoes or even volcanic islands are stable and calm but sometimes if they build up a caldera and store up kinetic energy they could suddenly without warning erupt causing tsunamis even more destructive than those caused by earthquakes. One example of this is when the Greek island Thera erupted violently in 1500BC which caused the end of the Minoan culture, and even possible was the mythical Atlantis, Thera is now known under the name Santorini.
The crater caused by the volcanic eruption of 1500BC is still visible today as on this landsat satellite image of the island of Santorini, Greece.
With out a doubt these have would be the most devastating types of tsunamis, if a large meteor or comet hit the open oceans, which it most likely would due to the fact that about 71% of earth is covered by oceans, it would actually be far worse for meteors or comets to hit the oceans rather than if it hit a large continental land mass because of the direct destructional force caused by having the kinetic energy transfered in the sea. Luckily most meteors that hit Earth are too small to cause damage, and there is actually something our governments could do to take preventative measures against major comets and asteroids becoming extinction event class meteor strikes.