• Analyze network problems.
• Detect network intrusion attempts.
• Gain information for effecting a network intrusion.
• Monitor network usage.
• Gather and report network statistics.
• Filter suspect content from network traffic.
• Spy on other network users and collect sensitive information such as passwords (depending on any content encryption methods which may be in use)
• Reverse engineer protocols used over the network.
• Debug client/server communications.

• A packet sniffer for a token ring network could detect that the token has been lost or the presence of too many tokens (verifying the protocol).
• A packet sniffer could detect that messages are being sent to a network adapter; if the network adapter did not report receiving the messages then this would localize the failure to the adapter.
• A packet sniffer could detect excessive messages being sent by a port, detecting an error in the implementation.
• A packet sniffer could collect statistics on the amount of traffic (number of messages) from a process detecting the need for more bandwidth or a better method.
• A packet sniffer could be used to extract messages and reassemble into a complete form the traffic from a process, allowing it to be reverse engineered.

Information from http://en.wikipedia.org/wiki/Packet_sniffer.