Use tcpdump, this is a neat utility, allowing you to scan every network traffic, that is present on your system, be it local network or localhost packets for internally running servers, every packet can be captured and analysed.

The most popular commands I recommend to use:

tcpdump -i eth0 port not 22
Show the traffic on your machine, excluding port 22, that you likely use for ssh, interface eth0
tcpdump -i eth0 icmp
Capture Ping packets and display them
tcpdump -i eth0 -s 65535 -w capture.pcap
Capture all traffic on eth0 and store into the file for analysis with Wireshark

Common cases to apply tcpdump: if you are not able to connect to a machine, but you do not know why. Routing or one way traffic problems can be easily noticed.

From time to time, you would want to see the contents of packets to understand what kind of data is being transferred and if the payload is correct. For this purpose you should capture the traffic into a pcap file and analyse it with Wireshark.

Despite the name, the command will let you monitor UDP traffic along with ICMP. Due to a stateless nature of UDP, it might be the best way to receive a confirmation of UDP flow.