What is an example of a non-relational database? Where/how are they used?

Question

I have been working with relational databases for sometime, but it only recently occurred to me that there must be other types of databases that are non-relational.

What are some examples of non-relational databases, and where/how are they used in the real world? Why would you choose to use a non-relational database over relational databases?

Edit: Two other similar questions have been mentioned in the answers:

• Database system that is not relational.
• Good reasons NOT to use a relational database?

Answer 1

• Flat file
  • CSV or other delimited data
  • spreadsheets
  • /etc/passwd
  • mbox mail files
• Hierarchical
  • Windows Registry
  • Subversion using the file system, FSFS, instead of Berkley DB