My startup Wizely has built its API on top of a Neo4j graph database. I've been working with it and the Cypher query language for over a year now and it's simply phenomenal. I've been using databases for decades and having used relational, nosql, hierarchical (old school), and now a graph database, it just adds another tool in my toolbox for solving problems effectively.
Is there a particular problem that you were able to solve with a graph database that would have been more difficult using a different database?