Is there a way to determine what application wants Java installed?
I did some more research and finally found some things out:


I have the Logitech remote software installed, and when launching it, it brings up the prompt, but a slightly different one. So, I know I have a few Java apps installed, but this was happening without me launching something
My actual error was related to a Facebook chat thing I had installed a while back, that I never put on my iMac. It was named 'com.facebook.videochat.[username].plist', and was in my ~/Library/LaunchAgents directory. 
I actually came across this question (asked after mine) when searching for the only Java information I found Console.app:


  8/31/12 6:44:23.606 PM Download Java Components[7588]:
  com.apple.message.domain:
  com.apple.java.usage2.DownloadOnDemand.complete
  com.apple.message.result: failure com.apple.message.signature:
  install_canceled com.apple.message.domain.version: 12A269

I would recommend checking your ~/Library/LaunchAgents directory first, and you can easily grep for java by doing: cd ~/Library/LaunchAgents and then grep -i "java" *.*. This searches for the word java (case insensitive) in all files in that directory. Thats where I found the reference to the Facebook videochat plist.