Neo4j seems to have the biggest mindshare among graph databases.
TitanDB, until it was acquired by DataStax, was a leading graph database.
DataStax Enterprise Graph is based on Titan. DataStax has different integration plans in store.
GraphX is an open-source graph computation framework for Apache Spark. According to Cloudera's Sean Owen, however, it's not getting much traction.
Gaffer is a graph framework released as open source by GCHQ, the UK Government Communications Headquarters, one of the three UK Intelligence and Security Agencies, along with MI5 and the Secret Intelligence Service (MI6).
Apache Giraph is an iterative graph processing system built for high scalability.
SAP Hana also supports graphs.