On a 64-bit Windows system you've got to install a 32-bit Java because OpenOffice for Windows is a 32-bit application. There is nothing wrong with installing as many Java runtimes as needed to run all your applications.
At the time of writing, this is the link from where you can download a Java Runtime Environment that differs from the automatically suggested download (e.g. Windows 64-bit): https://java.com/en/download/manual.jsp
The JDK (development kit) for Java developers can be used as well but it is a much bigger download. LibreOffice 5 for Windows is availlable as 32-bit and 64-bit application, so you don't need additional 32-bit Java for a 64-bit LibreOffice 5.
Edit 2022-03-12: https://adoptopenjdk.net/ provides Java runtimes for all platforms 32-bit and 64-bit
Combinations of Windows, Java and Open/LibreOffice:
64-bit Java on 64-bit machine: C:\Program Files\... works with 64-bit LibreOffice
32-bit Java on 64-bit machine: C:\Program Files (x86)\... works with OpenOffice and 32-bit LibreOffice
32-bit Java on 32-bit machine: C:\Program Files\... works with any installable office
64-bit software on 32-bit machine: impossible to install
The "Visual C++ Runtime" by Microsoft needs to be updated to the most recent version. This is also recommended for countless other applications regardless of the programming language.
http://www.microsoft.com/en-us/download ... px?id=5555 (32 bit aka "x86")
http://www.microsoft.com/en-us/download ... x?id=14632 (64 bit)
MacOS only at the time of writing (2015-03-18)
Recent versions of AOO and LO for the Mac are 64-bit versions anyway. If you encounter problems with the latest Java 8, make sure that you have the original MacOS version of Java 6 installed. Reference: https://bz.apache.org/ooo/show_bug.cgi?id=126130#c20
Install the JRE package of your distribution and any office suite which matches the bitness of your system.
There is a glitch in the Java section of the OpenOffice options dialog. When you select the right Java version from a list box with leading radio buttons, you've got to take care that you actually click the radio button within the list box. Just clicking the list box entry does not select anything.
|Edit: 2015-07-19: The major glitch with that list box is that it lists incompatible JREs among the compatible ones, particularly it lists 64-bit JREs that are incompatible with OpenOffice on Windows. Below the box you see the path of the currenly selected JRE. The path of a 32-bit JRE on a 64-bit Windows system usually starts with "C:\Program Files (x86)\" whereas the 64-bit JREs are stored under "C:\Program Files\". This is not a problem with 32-bit Windows systems where you can install 32-bit software only. The program path of a 32-bit Windows always starts with "C:\Program Files\"|