(covers information from several alternate timelines)
An access port was any type of panel which granted access to another area on a starship or space station, or to a computer interface. Such access ports were built into holodecks, for use in accessing ship's systems from within the holographic environment. (VOY: "Bride of Chaotica!")
Aboard the Earth Cargo Service freighter ECS Fortunate, Nadine was hiding in an access port while playing hide and seek with two boys. She was discovered by T'Pol. (ENT: "Fortunate Son")
In 2152, Commander Charles Tucker, chief engineer of Enterprise NX-01, located an access port to a cooling duct in the automated repair station at which the ship had docked, with which to access the main computer of the station. Entering the duct with Lieutenant Reed, the two Enterprise crewmembers approached to within twenty meters of the computer, before being beamed back to Enterprise by the station's artificial intelligence system. (ENT: "Dead Stop")
During a raid on an Illyrian starship in early 2154, Commander Tucker noticed an access port that he had to get to and pointed it out to the leader of the boarding party, Captain Jonathan Archer. After MACO Corporal R. Richards cleared the way to the access port by rendering two Illyrians unconscious via detonation of a stun grenade, Tucker and MACO Corporal Kelly rushed through the access port and then up a ladder. (ENT: "Damage")
In 2371, there was no access port or computer panel to enter a magnetically sealed comapartment aboard the Amargosa observatory, but Data was able to reverse the sealing's polarity, (Star Trek Generations)
In 2372, newborn Naomi Wildman was hidden inside an access port in USS Voyager's sickbay, when an out-of-phase version of the ship was boarded by Vidiians. (VOY: "Deadlock")
In 2375, while attempting to distribute a chroniton serum throughout the Voyager, which had been shattered into multiple time periods due to a chronokinetic surge, Commander Chakotay and Captain Janeway utilized an access port in the holodeck, injecting the serum into the port so that it would filter through to other systems. Their efforts were eventually successful in bringing Voyager back into temporal sync, and Chakotay was able to avert the accident which caused the fragmentation in the first place. (VOY: "Shattered")