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How much overhead is there that we can shave off to reduce latency until we really hit the limitations of speed of light? I mean, how much of the cross-continent latency is due to network gear or media changes (optical <-> electric) or even inefficient routing? Germany to linux.org.au is 310ms, so how much can we shrink that before the laws of physics get in our way?
>> round(c*0.31/1000)

ans = 92936 (kilometers)

Earth is about 40,000 km in circumference, so there's about a factor of four left to win on that particular hop.

Speed of light within a fiber optic cable is about c/1.5, so closer to a factor of 3. Throw in various continents that need to avoided, I'd guess it would be closer to factor of 2 in practice.
You are forgetting to account for the refractive index of the fiber and the fact the light reflects on the inside of the cable which lengthens the path it takes.
The speed of light through fiber is about 1/3rd slower than air, this makes the biggest impact to latency over distance. This is why microwave radio is sometimes used where speed is more essential than bandwidth, for example companies have established microwave radio links between Chicago and New York for trading for this reason.

New advances such as hollow core fiber might change this equation, because from a simple perspective, they essentially act like hollow wave guides that AT&T long lines was once building to carry microwave radio in tubes across the country (making them impervious to atmospheric issues, etc). I don't know too much about the practicality of using this kind of technology yet over global distances.

Another thing to watch for of course is SpaceX's plans to build a constellation of 4000+ communication satellites. They will be using "free space" like optics. Essentially in space you know where everything is, you don't need to use radio, you can point lasers between all your satellites and use tracking to keep them aligned. This provides huge bandwidth for them when you consider all the multiple paths between the 4000+ satellites. Plus because its traveling at the speed of light it will be ~50% faster than packets traveling through submarine cables. This might end up being the winning solution for reducing latency in global distances IMO.

Umm, doesn't the signal has to go up to the satellite, and then back down? That is not good for latency. You can see numbers like >1s round-trip time.
Well there is big gain if you learn how to use neutrinos and can communicate directly, not limited by Earth curve.

Earth diameter: 12742km

Speed of light in vacuum (and neutrinos): 299792458 m / s

One way communication between the worst two point on earth: 42ms

Ping: 85ms (most of places will be way faster)

High Frequency Trading folks are probably already getting excited :-P.

The earth is 134ms 'round' at the speed of light. There's quite a bit of room for improvement.
More like 192ms at the speed of light in optical fiber, before you start talking about regeneration, etc. but yes, plenty of room to innovate.