You must restart your system

In the 10 years that I've seen dialogs like these, I've always clicked "No" or "Restart Later" and the software ALWAYS works. The software installs indicate it's mandatory, but never is it functionally mandatory. Not TortoiseSVN, ISO mounting utilities, not even Microsoft Office; it always works without a reboot.
So why is this pattern so widely adopted?
Follow me on twitter: @paul_irish
It actually is mandatory.
According to Windows file locking semantics, a file in use cannot be modified or overwritten. Tortoise installs a shell extension to Windows Explorer which displays a special context menu, and that extension is a DLL file that is always loaded by Explorer. When the Tortoise installer attempts to overwrite this DLL with a newer version, it cannot (as the file is in use by Explorer) so it adds this file to a list of files to be overwritten on the next reboot, and prompts you to reboot at the end of the installation process.
You may not suffer any ill effects from not rebooting (the old shell extension DLL may work just fine for you, and still work with the new version of Tortoise you just installed), but a reboot is still necessary to complete the installation.
POSIX/UNIX file locking semantics are completely different - you can overwrite/change files in use. Next time the file is read, the new version if used, but for processes that are already running, the old one is used until the file handle is closed. Also, UNIX has a long tradition of having a "reload" command implemented, which causes the application to reload settings and other dependencies without restarting, so Tortoise on a POSIX system (like OS X or Linux) would simply overwrite the file, and ask the process which uses that file to reload, and never need to reboot. Rebooting has traditionally been completely unacceptable on UNIX, so they've got this stuff figured out… and that's why Windows is the only OS that requires users to reboot all the time.
I guess your and my definitions of 'mandatory' are different. I would expect 'mandatory' would mean I can't run the application until a restart has completed. That is obviously not the case, I'll just lose out on some eye-candy until next reboot.
@Paul Irish
You can also end up with instability, missing features, corrupted data, etc :-)
Imagine you upgraded to a new version that changed file formats. If you don't reboot, some components will be using the old file format, and others the new one. That could lead to crashes, or incorrect data being shown to the user. If there are components that perform writes, you could end up with data loss.