There are hundreds of ports and services registered with the Internet Assigned Number Authority (for the complete list, some 280kb, look here). Less than one hundred are in common use.
Services have assigned ports so that a client can find the service easily on a remote host. For example, telnet servers listen at port 23, and SMTP (Simple Mail Transport Protocol) servers listen at port 25, DNS servers at port 53. Client applications, like a telnet program or mail reader, use randomly assugned ports typically greater than 1023.
Although a particular service may have an assigned port, there is nothing about TCP/IP to prevent most services from listening to another port. A common example of this is HTTP, the protocol used for accessing Web servers. The assigned port for HTTP is port 80, but other ports, 8080 for example are relatively common. An intruder who sets up a backdoor may use an assigned port for an unregistered service (like a program that provides a root shell on demand), or the intruder may put a service, like a telnet server, on some other port than port 23. In other words, there is nothing sacred about port numbers--it is just customary to use them, as well as making things a lot simpler.
The purpose of this table is to list some of the port addresses associated either with popular services, or port addresses associated with services that have often been abused in the past. This list is by no means complete, but has in the past proven to be helpful. For example, if you have set up a firewall, and are noticing lots of connection attempts to port 113/tcp, you might be worried about an attack. But port 113/tcp is used by mail transport agents (sendmail in particular) in an attempt to identify the name of the user sending email.
Note also that many port addresses appear twice: once for a TCP-based service and again for a different UDP-based one. In the past, the custom was to allocated each type of port independently, so port 514/tcp belongs to the remote shell (rsh) and 514/udp is used by the system logger (syslogd). More recently, ports of both types have been assigned together, for example, ports 135, 138, and 139, both TCP and UDP, are assigned to Microsoft services.