When is it necessary to reboot an Ubuntu system?

• After kernel panic;
• After partitioning or filesystem modifications (more specifically, resizing root partition; I'd recommend to avoid resizing the hard drive from which you boot in general, regardless of partition; if you are resizing something external, like SD card or USB, no reboots necessary );
• After kernel upgrade and security patches (although that might not always be necessary);
• After system became unresponsive for whatever reason, and you've no option but to use magic SYSRQ keys or hard reset
• After making changes to some dconf schemas , depending on the way application may have been developed. Related answer
• Your CPU is overheating (you don't wanna keep on roasting those cores, do you ?)

There are generally two situations where a reboot is usually necessary:

1. The kernel is upgraded.
2. libc (rather, glibc) is upgraded.

There is a mechanism for reloading the kernel without restarting (How can I upgrade my server's kernel without rebooting?). With glibc, the biggest problem is init. It is possible to restart init (see Restarting init without restarting the system).

For the average user, neither is recommended, and restarting is necessary.

Apparently, there exists a third case:

3. dbus has been upgraded. dbus-daemon is apparently incapable of restarting (from what I can understand of the discussion on this LWN article). And since a lot of things rely on DBus...

Actually, it depends what you're trying to accomplish:

• If you do an apt-get dist-upgrade and a new kernel comes in, and you want to activate it, you need a reboot.

• If a new version of FireFox comes in, you obviously don't.

And in between those two extremes are 50 shades of grey:

;-)