To print packets on all network interfaces (it's often best to pass -n to display IP addresses rather than hostnames):
tcpdump -ni any
To print all packets on port 8080:
tcpdump port 8080
To print all sent to or from 192.0.2.1:
tcpdump host 192.0.2.1
To print all packets sent from 192.0.2.1, excluding on port 22:
tcpdump src host 192.0.2.1 and not port 22
To write all packets on port 8080 to out.pcap:
tcpdump port 8080 -w out.pcap
To print the start and end packets (the SYN and FIN packets) of each TCP conversation.
tcpdump 'tcp[tcpflags] & (tcp-syn|tcp-fin) != 0'
To print all IPv4 HTTP packets to and from port 80, i.e. print only packets that contain data, not, for example, SYN and FIN packets and ACK-only packets.
tcpdump 'tcp port 80 and (((ip[2:2] - ((ip[0]&0xf)<<2)) - ((tcp[12]&0xf0)>>2)) != 0)'