Yes, it's very widely used at Google through Chubby, which underpins many core pieces of infrastructure, including name resolution. (It used to be common practice to depend more directly on Chubby for synchronization of state via shared global files, but that fell out of favor about 6 years ago due to reliability risks associated with just blasting out changes globally without any canarying.)
https://en.wikipedia.org/wiki/Paxos_(computer_science)#Produ... lists a bunch of other use cases (notably, Google's Spanner and Amazon's DynamoDB).
> And let me ask the same question for all other academic distributed algorithms right away.
Raft (designed as a more understandable alternative to Paxos) is more commonly used, as I understand it.
https://en.wikipedia.org/wiki/Raft_(algorithm)#Production_us...
> I recall seeing a study some 10 years ago checking the major cloud providers for Byzantine fault tolerance and finding none of them to exhibit the qualities that the known algorithms would guarantee.
I'm curious which study you're referring to. I could believe that while Paxos might be used as a building block, it might not be used in a consistent manner throughout.
Also, note that not all of the variations of Paxos handle Byzantine faults.
I can't find the study any more, though I'm pretty sure I saw it on HN...
The paper itself is very approachable and worth spending an hour or so on.