Such a wave travels at well over 800 kilometres per hour (500 mph) -quoted from wikipedia http://en.wikipedia.org/wiki/Tsunami

It's not a wave that physically moves as a single mass of water across the ocean. It's a shockwave that propagates through the ocean.

It's not a shock wave, it's a shallow water wave (because the wavelength is much larger than the depth of the ocean). The speed depends on depth [v = sqrt(g*H)]; for typical deep Pacific (5000 m), that is ~220 m/s or 500 mph.

I don't think there are waves that move "as a single mass of water across the ocean." or through any other medium. http://en.wikipedia.org/wiki/Waves:

"The term wave is often intuitively understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole,"

For an analogy with (not quite an explanation, as the mechanisms are a bit different) a tsunami's speed, think of what happens when you pluck a guitar string. The back end of the string starts moving up before you even release the string. So, say you lift a string at, say 1cm/s for .1 of a second. (Almost) at the end of that 0.1s, the start of the wave that will form has reached the other end of the string, moving at meters per second (the 'almost' is because the string will deform. Ultimately, relativity has something to say here, too, but that only matters when the resulting wave signal would move near the speed of light)