Also worth pointing out that other types of graph database exist, for example those that follow the Resource Description Framework (RDF) model, commonly known as Triple/Quad stores.
They have the benefit of a W3C standard query language behind them (SPARQL[1]), a defined RESTful protocol[2] and quite a few databases available, both open source and commercial, that have some benefits over Neo4J - for example the ability to scale out with a shared nothing architecture (MarkLogic, Virtuoso Cluster Edition and 4Store).
It all depends on your workload, of course, and for some people the RDF model won’t provide all they need, however, it’s a powerful model and worth exploring if you’re thinking of using a graph database in an upcoming project.
[1] http://www.w3.org/TR/sparql11-query/
[2] http://www.w3.org/TR/rdf-sparql-protocol/