There doesn't even seem to be the option in Safari. And while the Java plugin is installed on Firefox, it doesn't work there either, which makes me think it might be a system-wide issue. I do have Eclipse and a few other Java applications on my computer, and they all work fine.
I looked all over the place, and I found out that Java should be an option in the preferences window in Safari, but it's not there:
Best Answer
In additition to Martineau's response I had to set the Security Level slider to Medium in order to run applets that do not have a certificate from a trusted authority.