I would like to try out Oracle VM just for fun.
Can it be downloaded for free from Oracle?
And if so, does anyone have a link?
You can get it from the Downloads link on the Oracle VM home page. Choose Enterprise Linux & VM from the Downloads menu. Or this link will take you right to it. Note you'll have to register as part of the download process.
(Also worth noting that VirtualBox is now Oracle's product and is free to download)
Developers can download copies of the Oracle server, and the Oracle VM lives inside there.
This answer, while accepted, is sadly completely wrong. I was mislead by a comment into thinking that the JVM was at issue.
I can't delete it because it's accepted.