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: 
If performance is an issue, consider whether you need all of the strong consistency guarantees Paxos gives you. See e.g. <http://queue.acm.org/detail.cfm?id=1466448> and <http://incubator.apache.org/cassandra/>. Searching on Paxos optimised gets me hits, but I suspect that relaxing some of the requirements will buy you more than tuning the protocol.
Google documented how they did fast paxos for their megastore in the following paper: [Link](http://static.googleusercontent.com/external_content/untrusted_dlcp/research.google.com/en/us/pubs/archive/36971.pdf).