I updated to Ubuntu 12.04 and now Eclipse does not accept OpenJDK 6 in /usr/lib/jvm anymore. I tried to install openjdk 7 and it did create two folders in /usr/lib/jvm, but neither is accepted by the Eclipse JDK dialog.
Edit: I am referring the the JDK that is used to compile and execute the written programs. Not the JRE used to run eclipse. This especially means that using the proprietary JDK is not an option for me.