SNOWWHITESICKETTE  Software Update won't tell you about the Java 9 release unless you have the Java 8 release installed. Don't know why it didn't tell you about the earliest one you didn't have. That's the case with all Apple software, Software Update doesn't tell you about new stuff if it requires something else you have not installed. I have installed Tiger about five times on four Macs within the past six months, and noticed that Safari was not listed in Software Update. Tiger came with Safari 2. I installed Safari 4 anyway. On one machine, I installed Safari 3.x and then Software Update told me about Safari 4.

On the other hand, iTunes recommends the latest iTunes 9 for my G3 iMac and iBook that are below the technical requirements. Software Update has not done that, thankfully. (I forgot to uncheck the box in iTunes that allows it to check for updates.)

Have you tried running the 10.4.11 Combo Update again? If you are having issues with the OS software, running the update again fixes some problems. I have done that once, and it fixed the problem I had, and caused no new problems.  
(Version Release 9)

SNOWWHITESICKETTE  Also wanted to say, yes it's good to have the latest version of Java that is available to you. Sometimes there are improvements, and sometimes there are security fixes. The main place I encounter Java is an online game site I play at, and having the latest version is necessary. I have not had problems with Java updates, they haven't messed up anything (yet). I like Java a lot better than Flash.  
(Version Release 9)

SNOWWHITESICKETTE  Back again, with something that actually might help. (If you have not fixed the problem already.) Look in the main folder that says Library, and you will see a subfolder named Receipts. Check for the following items (but don't try to open them, or move anything):

Java.pkg

Java131and142release2.pkg

J2SE50Release3.pkg

J2SE50Release4.pkg

JavaforMacOSX10.4Release5.pkg

JavaforMacOSX10.4Release6.pkg

JavaforMacOSX10.4Release7.pkg

JavaforMacOSX10.4Release8.pkg

JavaforMacOSX10.4Release9.pkg

Java.pkg is included with Tiger, I believe. The others are all available at Apple's website, under Downloads. You will have to search for them, because some of them are old. (Leave off the .pkg if you search for them.) The order listed would be the installation order, but I don't have Release 3 installed on my machines. This may be because a later version replaced it. Software Update didn't bring it to my attention, and my Java works fine. To be on the safe side, download anything in that list you are missing, and start installing them from the earliest one to the latest. Repair permissions with Disk Utility first, and you can repair permissions between them if you want. (If I recall, one of the last two actually did need permissions repair, but the rest did not.) Some of the downloads are sizable, near 100 MB, so it will take some time to get everything done. Hope this helps.  
(Version Release 9)

YELLEKO  Many thanks. I'll look into all this.  
(Version Release 9)

SNOWWHITESICKETTE  You're welcome. : )  
(Version Release 9)

ESPECTRO  You don't see any changes because you are not using Java 2 Version 5 version 1.5 update 02 build 36

The install won't change your default java version, and the included app doesn't change it either, it just changes the version for the java plugin. If you want to use it you have to get dirty on the command line and backup the CurrentJDK symlink in /System/Frameworks/JavaVM.... to match the new version  
(Version 5.0)

VIELNUTZER  If NeoOffice is working this would be a great news for all users. What do you mean with prefs app. Could you please tell in a few words what you realy did running NeoOffice? It is important for our school network but we running a german system. Regards   
(Version 5.0r4)

VIELNUTZER  Sorry I did not see the date, it is late and I was looking for Office on Intel Mac. Bye I go to sleep  
(Version 5.0r4)

YOXI  It's not possible to change the java version NeoOffice uses - NeoOffice/J (v1.1) will only use v1.3.1, NeoOffice (v1.2) will only use v1.4.2 (and is thus only compatible with OSX 10.3 upwards). If you change the default java in your OS to 1.5, NeoOffice will not work, but as the other poster said, it's a more under the bonnet job to change the system's default java version.  
(Version 5.0r4)