How can I know if reboot is required after update?
Solution 1:
Check checkrestart from the debian-goodies package.
It shows which processes using the old versions of the libs you updated.
If you are not able to remove all processes out of that list, you need a reboot :)
Additionally (as YuKYuK said), always reboot after a kernel update!
Solution 2:
cat /var/run/reboot-required.pkgs to see 'service' waiting for a reload. Nothing needs a reboot, only kernel upgrade (and Windows :) ).
Or on Debian: lsof | grep lib | grep DEL