The most common case is a new kernel as far as I know, but what are other cases that usually require a reboot, too?
require, no, it's VERY tricky to update the kernel on a live system, but possible. most of the software works with the same config files, so would simply need an install of the update, restart the scripts for the daemons/programs to update, then removal of the old version.
i can't really think of anything past changes to things plugged directly into the motherboard(cpu/ram/cards) that would need it, and if the hard drive adapter supports hotswap you might even be able to change root to an entirely different os on a live system.
i guess you're asking so you can do stuff to impress the ladies with your leet linux skillz, i don't think it'll work.
ok, maybe elf libraries, but linux seems to have been designed to make windows users go 'why can't my computer do that?!'.
Create the cluster and restart nodes if necessary. One machine? You will have to virtualization and cluster again. This approach does not depend on the types of operating systems. And worst of all, it works).