This is an interesting question to answer accurately as you have to consider a few different ways to define it.
If we want to know which country records the
earthquakes, then that would be Japan. The entire country is located in an area of high seismic activity and they have the densest seismic network, so they are able to record many earthquakes.
Indonesia on the other hand actually has the most earthquakes as it is much larger in size, and spread over a wide area of seismic activity. However, they have more sparse seismic instrumentation, so some of the smaller quakes may not be recorded.
The majority (almost 75%) of the world's seismic energy is released at the edge of the Pacific, where the thin Pacific tectonic plate is forced beneath the thicker continental crust along what is known as 'subduction zones'.
This has created a 40,000km strip of high risk seismic areas which stretches up the west coasts of the Americas and from the northern USA to Alaska, and on to Japan, China, the Philippines, Indonesia and Australasia. This is definitely the most active area for earthquakes.