That's tough to answer without knowing more about what type of communications you're trying to block and why. Generally, the best way to block traffic is to use a firewall. However, low-end firewalls (such as Internet Connection Firewall) are usually not capable of per-IP filtering.
The poor man's way to block an IP is to adjust the routing tables on your computer. The ROUTE command-line tool can do this. This is not an easy tool to use, and making changes to it without understanding routing can cause your computer to lose its ability to connect to the network. With that said, a command such as the following would block communications for the IP address 10.121.187.13:
route –p add 10.121.187.13 MASK 255.255.255.255 192.168.1.0 METRIC 1 IF 2
You'll need to change the interface number to match your computer's interface, and the destination IP to something on your local network that doesn't exist. Like I said, there's no easy solution.
This was first published in October 2003