The Earthquake in Southeastern Asia is, first of all, a sad event for the people there, and it is sad for all of us. Tens of thousands of lives were suddenly ended by evil, despicable acts of mother Nature.
I always wondered whether it's possible to escape from these tsunamis. But it's not realistic. The waves on the ocean have very different dispersion relations from the electromagnetic waves, for example. More precisely, the speed increases with the size of the waves. (Well, it's not just about the dispersion relations because the waves behave non-linearly as a function of their amplitude.) The ideal approximation of tsunami is the so-called "shallow-water wave" in which the speed is sqrt(g.d) where d is the water depth.
It just happens that these waves that can be as high as 10 meters propagate with the speed about 300 miles per hour - something like 120 meters per second. Now if you're enjoying the Sun on the beach, you only see the wave when it's one mile away or so, and therefore you have something like 10 seconds to run. It's very hard to run in the sand, so perhaps it's better to give up immediately. You just can't escape from a wave which is 10 meters in height unless you are a highly intelligent squirrel that can quickly climb a sufficiently massive tree or unless you see a staircase nearby. Well, what I just wrote is not quite true because the waves usually slow down to about 30 miles per hour when they approach the land, because of the dependence on the water depth mentioned previously, and therefore you can actually have a minute to leave...
There are also some warning systems (one still has a few hours before the wave reaches the shores), but unfortunately they were not used in this case: tsunami are not too frequent in this are and the people are too poor to organize some high-tech security systems. Tsunami means "wave in port" or "harbor wave" in Japanese.