I guess that you really meant to ask "Are Sun's JRE and JDK open source?". The answer to that question is as Campbell already said: almost, but it's not completely open source yet. Almost all code of Sun's JRE and JDK has been open source, but Sun used some third-party code in their JRE and JDK that they cannot make open source, because they don't have the rights for it. Currently there are a number of people working to replace that code with open source code, so that it will be completely open source.
Note that there is already a 100% open source Java, called GNU Classpath. But it's only a partial implementation of Java 1.4 and it runs very slow compared to Sun's Java.