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: 
Not sure if this is helpful (since this is not from actual production information), but in our "distributed systems" course we've studied, along with Paxos, the **Chandra-Toueg** and **Mostefaoui-Raynal** algorithms (of the latter our professor was especially fond).
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.