If your kernel crashes every once in a while and you want to find out
what happened and/or create a good bug report so it can get fixed,
here's all you need to do in Ubuntu 12.04+:
sudo apt-get install linux-crashdump apport
This automatically installs and sets up a crash kernel to be loaded
via kexec in case of a kernel panic. And it installs apport to be able
to easily report the crash to Ubuntu. The logs will be in /var/crash.
Read here for more: https://wiki.ubuntu.com/Kernel/CrashdumpRecipe
And this ebook might help with debugging a crash:
Of course sometimes this might not work for very hard crashes. But
most crashes should be able to be properly dumped and reported this
way. Good luck!