Are Richter-magnitude 10 earthquakes possible? The largest earthquake since 1900 according to the United States Geological Survey (USGS) was Richter-9.5 magnitude quake in Chile in 1960. Are magnitude 10 earthquakes possible? If so, what is the most likely frequency of such earthquakes, and where are they the most likely to occur?
Adding a little bit of practical data to the above answer about the Gutenberg-Richter relationship, here is a plot of the per-year cumulative probability of earthquakes in a particular province in Japan, based on observed frequencies over many hundreds of years:



Source: http://topo.earth.chiba-u.jp/afr/backnumber/no24/24%E5%8F%B702kumamoto.pdf

The relationship is plausibly log-linear (in accordance with G-R); if you accept that the relationship will hold up to higher magnitudes, you would estimate the probability of a M10 event in this location at once every 30,000 years. 

To get an estimate for "anywhere in the world" you would need the cumulative data for all. A good place to start is the USGS website - they have a handy table with data since 1900.

Taking these data and plotting them on a log-linear graph, then extrapolating a linear fit, gives the following chart:



This is rather scary because it suggests that there is about a 1:100 chance of a M10 earthquake anywhere in the world, in any given year. Note that I plotted the data for magnitude x to x.9 at the location of x - which tends to underestimate things a little bit. Note also that at the extreme end of very large earthquakes (8 and above), the data looks like it might be deviating from the straight line - but there are not enough data points to draw any firm conclusions about the shape.

There are several other caveats. First - the assumption that the model can be extrapolated can be challenged: a particular fault may not be constructed in such a way as to store the energy required for an M10 event, as it will always release the energy before it gets there (and there may be a "stress shadow" effect, which says that after a big earthquake, the chance of another big one is temporarily reduced because stresses have been relieved; this is why this model can only be used "over a long period", and does not accurately reflect the risk of earthquake in the next five years).

Still - one percent.