For that matter, the Apache Software Foundation has a Java implementation called 'Harmony', although I'm not sure they're allowed to call it Java.
That is a sadly long and storied history, which Stephen Colebourne describes best:
http://www.jroller.com/scolebourne/entry/sun_apache_ip_in_pi...
There is some hope that the legal shenanigans will stop once ORCL finishes taking ownership of JAVA.
BEA has its own JVM as well, and guess who bought BEA?
http://www.oracle.com/technology/products/jrockit/index.html
By the way, I think JRockIt is the best JVM out there for server-side deployments. I've used both JRockIt and Sun's JVM on EC2, and JRockIt has much better memory management.
https://www.ibm.com/developerworks/java/jdk/