cybersam February 2016
The neo4j Browser has an Export menu in the group of menus on the top right of every result pane. It can export the results to a number of different formats, including CSV.
You can use the neo4j-shell-tools, which can export to CSV.
Both of these techniques require that a neo4j server is running with your DB.
Also, they require a Cypher query that returns all the data.
For example, this query should return all data (all relationships, and all nodes that either have or do not have outgoing relationships):
OPTIONAL MATCH (n)-[r]->()