Should I restart my PC every time it gets updated?
You do not have to restart your computer every time you update. Certain updates (such as those that affect your operating system kernel) will require rebooting to take effect. When such an update occurs, your session icon in the upper-right will glow red.
You only need to restart when the update manager tells you to. It will also be visible in the menu on the top right of your screen. The cog will be red and a red menu item will ask you to restart.
You dont 'have' to restart, but the only time you have to restart for changes to take effect are kernel upgrades and proprietary driver upgrades.
There is another way.
Ksplice allows you to update your system -- even kernel updates -- without restarting.
It is free for Fedora and Ubuntu Desktop, but you pay for any other system.
Once in awhile a program running on your system gets upset because some parts of it have been updated, but, usually, all you have to quit the program and restart it. Other than kernel updates as mentioned above, you don't need to restart.
A major factor in this more civilized behavior is that Linux/UNIX doesn't have a registry system like Windows does. I don't know the exact mechanics of it, but Windows keeps its registry locked up when it's running and, often, the only way to modify it is to restart the system so changes to the registry can get installed while it's not being used.
On the other side of the coin, if you do upgrade your kernel, some programs that you may have compiled yourself (e.g. by running make with a package that came in a tarball) may stop working when you upgrade a kernel until you recompile them. vmware player is like this although it sometimes fixes itself. This is part of the reason boot loaders like grub keep old versions of the kernel as startup menu options.
Unless you seldom do updates, and then do a large number (eg. monthly). Then it is prudent to re-start, etc.
You should restart when kernel updates, or when driver was updated. Otherwise kernel or driver update won't work until reboot.
I would say for security updates you should depending upon the severity of the vulnerabilities that the updates resolve.