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.
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.