Question: I've read Lamport's [paper](http://research.microsoft.com/en-us/um/people/lamport/pubs/paxos-simple.pdf) on Paxos. I've also heard that it isn't used much in practice, for reasons of performance. What algorithms are commonly used for consensus in distributed systems?

Answer: 
You should check the Apache Zookeeper project. It is used in production by Yahoo! and Facebook among others.

<http://hadoop.apache.org/zookeeper/>

If you look for academic papers describing it, it is described in a paper at usenix ATC'10. The consensus protocol (a variant of Paxos) is described in a paper at DSN'11.
[Raft](https://raft.github.io/) is more understandable, and faster alternative of Paxos. One of the most popular distributed systems which uses Raft is [Etcd](https://github.com/etcd-io/etcd). Etcd is the distributed store used in Kubernetes. 

It's equivalent to Paxos in fault-tolerance.