Windows Vista :If I have a router with a built-in firewall, should I also turn on Windows Firewall?

Yes, because router-based firewalls only provide protection from
computers on the Internet, not from computers on your home network.
For example, if a mobile computer or guest computer connects to some
other network, becomes infected with a computer worm, and then
connects to your home network, your router-based firewall won't be
able to prevent the spread of the worm. However, a firewall running on
each computer on your network can help control the spread of worms.