First, use encryption! If you encrypt sensitive data and passwords while in transit, you'll render packet sniffers useless.
Encryption can be implemented in a number of ways: SSL (HTTPS) connections to Web servers, encrypted SSL or TLS connections to mail servers, or other application-specific techniques. Alternatively, you can use a virtual private network (VPN) to encrypt entire communications links, regardless of protocol.
Second, use a switched network. In this case, a packet sniffer will only be able to eavesdrop on connections taking place on its own local switch port. If you assign each system to an individual switch port, there simply won't be any packets for the packet sniffer to intercept.
This was first published in April 2007