The version of Java you should use depends on the Aspire version you are targeting:
Note: We recommend installing the Java JDK (Java Development Kit), just in case you want to create your own Aspire components/applications in the future. However, only the JRE (Java Runtime Environment) is absolutely required.
1. Download and install the latest version of the Java 1.6 or 1.7 JDK as appropriate: http://java.com/en/download/manual.jsp