Most people are familiar with the netstat command on Windows and UNIX-like systems, which lists the open TCP and UDP ports as well as current TCP connections. Cisco IOS provides a similar command: show control-plane host open-ports. Recall that a router's control plane is what handles traffic destined for the router itself, versus the data plane which is responsible for passing transient traffic. The output of this command is nearly identical to that of Windows' netstat -n:

Router# show control-plane host open-ports
Active internet connections (servers and established)
Prot        Local Address      Foreign Address                  Service    State
 tcp                 *:23                  *:0                   Telnet   LISTEN
 tcp                 *:80                  *:0                HTTP CORE   LISTEN
 udp                 *:67                  *:0            DHCPD Receive   LISTEN
 udp               *:2887                  *:0                      DDP   LISTEN

Above is the output for a default configuration running IOS 12.4(9)T1. We can see listed TCP/23 (telnet), TCP/80 (HTTP), UDP/67 (DHCP daemon), and UDP/2887 (WLCCP). Just like netstat, new TCP connections will be listed with a state of "established." Below an administrator has connected to the web configuration interface of the router:

Router# show control-plane host open-ports
Active internet connections (servers and established)
Prot        Local Address      Foreign Address                  Service    State
 tcp                 *:23                  *:0                   Telnet   LISTEN
 tcp                 *:80                  *:0                HTTP CORE   LISTEN
 tcp                 *:80       10.0.0.8:53743                HTTP CORE ESTABLIS
 udp                 *:67                  *:0            DHCPD Receive   LISTEN
 udp               *:2887                  *:0                      DDP   LISTEN

Disabling the web configuration service will remove TCP/80 from the open ports:

Router(config)# no ip http server
Router(config)# ^Z
Router# show control-plane host open-ports
Active internet connections (servers and established)
Prot        Local Address      Foreign Address                  Service    State
 tcp                 *:23                  *:0                   Telnet   LISTEN
 udp                 *:67                  *:0            DHCPD Receive   LISTEN
 udp               *:2887                  *:0                      DDP   LISTEN

Similarly, enabling a new connection-oriented service on the control plane will add additional ports. For example, BGP opens TCP/179 and initiates a connection with each neighbor:

Router(config)# router bgp 100
Router(config-router)# neighbor 10.0.0.2 remote-as 100
Router(config)# ^Z
Router# show control-plane host open-ports
Active internet connections (servers and established)
Prot        Local Address      Foreign Address                  Service    State
 tcp                 *:23                  *:0                   Telnet   LISTEN
 tcp                *:179                  *:0                      BGP   LISTEN
 tcp                *:179       10.0.0.2:15158                      BGP ESTABLIS
 udp                 *:67                  *:0            DHCPD Receive   LISTEN
 udp               *:2887                  *:0                      DDP   LISTEN

A similar command is show ip sockets on older IOS versions, but it doesn't seem to list TCP sockets. However, it will list other non-UDP protocols, like EIGRP:

Router# show ip sockets
Proto    Remote      Port      Local       Port  In Out Stat TTY OutputIF
 17   --listen--          --any--          2887   0   0   11   0 
 17 0.0.0.0             0 10.0.0.1           67   0   0 2211   0 
 88   --listen--          --any--           100   0   0    0   0