I went to Openoffice.org and blindly downloaded the default package "OOo_3.0.0_LinuxIntel_install_wJRE_en-US.tar.gz" which is the wrong package for Ubuntu 8.10.

The Fix:
Go back to openoffice.org, under "I want to download OpenOffice.org" click the "Get more platforms and languages" link and choose the package in your language under the "Linux DEB" column.
The correct package should have a filename something like "OOo_3.0.0_LinuxIntel_install_en-US_deb.tar.gz"
or
Even easier from a comment below (and you won't have to download a new OO install file)

sudo apt-get install rpm

If you don't you will run into all the errors I did below, save your self the hassles I got trying to get it to work:

Error:
user@mypc:~/Desktop/OOO300_m9_native_packed-1_en-US.9358$ ./setup Checksumming...
Extracting ...
./setup: 478: rpm2cpio: not found
cpio: premature end of archive
find: `usr/java': No such file or directory
basename: missing operand
Try `basename --help' for more information.
/dev/pts/0
Error: Failed to extract the Java Runtime Environment (JRE) files. (exit code 7)

Fix:
Install a jre and then point setup to it.
sudo apt-get install sun-java6-bin

Rerun setup with -j option:
user@mypc:~/Desktop/OOO300_m9_native_packed-1_en-US.9358$ ./setup -j /usr/lib/jvm/java-6-sun-1.6.0.07/jre/bin/java
Parameter: j
Using /usr/lib/jvm/java-6-sun-1.6.0.07/jre/bin/java
java version "1.6.0_07"
Java(TM) SE Runtime Environment (build 1.6.0_07-b06)
Java HotSpot(TM) Client VM (build 10.0-b23, mixed mode, sharing)

Running installer
/usr/lib/jvm/java-6-sun-1.6.0.07/jre/bin/java -DHOME=/home/user -DJRE_FILE=jre-6u7-linux-i586.rpm -jar JavaSetup.jar
System locale: en_AU
User privileges
OS: Linux
Mode: installation
Path to packages: /home/user/Desktop/OOO300_m9_native_packed-1_en-US.9358/RPMS/


Next error:
IOError: java.io.IOException: Cannot run program "rpm": java.io.IOException: error=2, No such file or directory
sudo apt-get install rpm

This time run it as root:
sudo ./setup -j /usr/lib/jvm/java-6-sun-1.6.0.07/jre/bin/java

Then you get this:
error: Failed dependencies:
/bin/basename is needed by jre-1.6.0_07-fcs.i586