Just curious. Also, what distributions ship with Java?
I think Mark has it backwards.
Regardless almost all distros will have Java & Mono available in the repositories somewhere. Fedora always comes with Java IIRC and Ubuntu derivitives usually come with Java, Mono is somewhat less used and therefor less included but apg-get install mono (Or whatever) and yum install mono will both set you on track depending on the repository system of your distro.
Also Ubuntu I believe has access to the "real" Java and fedora requires it be downloaded as an extra from Sun/Oracle. (I usually do this as a developer for testing but the OpenJDK/JRE which is also Oracle/Sun supported will work in 99.9% of cases and will be the only supported version after seven is released IIRC)