Researchers at the University of Utah have compiled the data and come to the conclusion that an earthquake can trigger other earthquakes thousands of miles away (even at opposite ends of the world (almost)).
When an earthquake happens, there are several different types of shockwaves released. The first waves sent out are called P-Waves (for pressure), which behaves much like a sound wave, only traveling through the earth insted of air. Alongside these, there are so called shear-waves, which are waves moving from side to side. Next are two types of surface waves, Love waves and Rayleigh waves (i recommend checking out the links for all these different waves, wikipedia has nice pictures explaining what types of waves these are).
Now enough with the boring definitions, the nitty gritty of it is, that they looked at the data for over 500 earthquakes, and found big increases whenever the surface waves (Love and Rayleigh) came over a certain area. To me this is pretty remarkable, as I’d imagine that these surface waves would be HEAVILY dampened by the time they reach those far-away places, and yet they are enough to trigger seismic activity. As an example, they noticed that the 2004 earthquake in Sumatra (that caused the Tsunami) managed to trigger earthquakes all the way over in Europe!
Now this is obviously all very cool, but they really do not know WHY this is happening yet. All they have done is look at the data and they can clearly see that the seismic activity is way up whenever those surface waves come knocking, but the actual physics behind it have not yet been determined. If you are interested in reading more about this (including a postulation on what might be the cause) you should check out their press-release.