tl;dr- You can create permanent walk-through-portals in both D&D 3.5e and Pathfinder. You can create a walk-through-portal in D&D 5e, but there doesn't seem to be a way to make it permanent.
D&D 3.5e: The Gate Key can make permanent portals
The Gate Key is an epic-level wondrous item that can do this:
When properly operated, the gate key can be used to attune any bounded space, such as a doorway or a cave opening, to another bounded space on another plane of existence previously visited by the wielder. When two bounded spaces are attuned, an interdimensional portal springs up at each location, and the two portals are connected. When the wielder creates a pair of portals, he or she also establishes the necessary key that travelers must have to access the portal. Possible keys include nothing, a pearl, a particular hair color, or even the gate key itself. Up to sixty different pairs of portals can be attuned in this manner. Once all sixty pairs of portals are created, the key cannot create additional gates, though it may still be the necessary key to access some or all of the portals. To any creature without the proper key, the interdimensional portals are not visible (through true seeing or similar magic reveals their presence).
So to have a portal open and visible to everyone, the "[p]ossible key" could be selected as "nothing".
This method is limited to making portals between different planes, rather than within the same plane. But since the same Gate Key can be used to create up to 60 portals, you can just connect 2 portals at an intermediate plane to get a connection between two points on the same plane.
Pathfinder: Greater Create Demiplane's Portal feature
Cast Create Demiplane, Lesser to create a demiplane.
Cast Permanency to make the demiplane permenant.
Cast Create Demiplane, Greater to add a permenant portal to a target location.
Portal: Your demiplane gains a permanent gate to one location on another plane, which can only be used for planar travel. This location must be very familiar to you. This gate is always open and usable from both sides, but you can secure it using normal means (such as by building a door around it).
Cast Create Demiplane, Greater again to add another permant portal to the other target location.
The spell description doesn't seem to give any constraints on where you can place a Portal, so presumably you could place two different portals right next to each other such that someone stepping through one automatically goes through the other.
Or if that feels a bit iffy, then you can:
Cast Create Demiplane again to give it the Structure feature and specify a solid tunnel connecting the portals.
Structure: Your demiplane has a specific, linked physical structure, such as a giant tree, floating castle, labyrinth, mountain, and so on. (This option exists so you can pick a theme for your plane without having to worry about the small details of determining what spells you need for every hill, hole, wall, floor, and corner).
Then if you want to customize anything, now'd be the time to do it. For example:
Cast Create Demiplane, Greater again, selecting the Energy feature,
Energy: Your plane gains the (minor) negative- or positive- dominant energy trait. A plane cannot have both the negative-dominant and positive-dominant energy traits.
to give the demiplane the minor Positive-Dominant trait,
A minor positive-dominant plane is a riotous explosion of life in all its forms. Colors are brighter, fires are hotter, noises are louder, and sensations are more intense as a result of the positive energy infusing the plane. All living individuals in a positive-dominant plane gain fast healing 2.
Undead instead take 1d6 points of positive energy damage per round, and at 0 hit points they crumble to ash.
, which could provide healing to travelers who go through the portal's tunnel (if there's a small gap between them). Or, other features, like doors, defenses, a Good-alignment trait, etc..
Finally, since the demiplane and its portals are permanent and can't be dispelled from the outside, the only way for someone to remove it would be to cast spells that destroy it from within:
The plane cannot be dispelled, but a creature on the plane can destroy it by using limited wish, mage’s disjunction, miracle, or wish and making a successful dispel check.
If you want to prevent this from happening, then you can:
Cast Create Demiplane, Greater one last time, after everything else is prepared, to give the demiplane the Magic feature,
Magic: Your plane gains the dead magic, enhanced magic, impeded magic, or wild magic planar trait. If you selected dead magic, you are trapped within your plane unless it has a permanent planar portal (such as the portal feature, below). If you selected enhanced or impeded magic, choose one type of magic to be enhanced or impeded, such as “effects with the fire descriptor or that manipulate fire” or “death spells and spells from the Death or Repose domains.” A plane cannot be enhanced and impeded for the same kinds of spells.
specifically to give it the dead magic trait,
These planes have no magic at all. A plane with the dead magic trait functions in all respects like an antimagic field spell. Divination spells cannot detect subjects within a dead magic plane, nor can a spellcaster use teleport or another spell to move in or out. The only exception to the “no magic” rule is permanent planar portals, which still function normally.
, which should prevent anyone from within the demiplane from being able to dispel it.
End result: Permanent portal that goes through a demiplane
In the end, you get a permanent portal that connects two locations of your choice. At your option, it can either appear to be a single portal, or you could have a tunnel-like portal. And if it's tunnel-like, you can put in defenses, locked doors, healing/damaging properties, etc..
Also, you could add additional Portal's to the demiplane, making something of a nexus that connects many locations.
D&D 5e: Can do a walk-through demiplane with 2 portals like Pathfinder, but lasts only 1 hour
D&D 5e has Demiplane, which also creates a demiplane with a "shadowy door" that sounds like a portal:
You create a shadowy door on a flat solid surface that you can see within range. The door is large enough to allow Medium creatures to pass through unhindered.
And apparently you can cast it a second time to get a second portal to the same demiplane:
Each time you cast this spell, you can create a new demiplane, or have the shadowy door connect to a demiplane you created with a previous casting of this spell.
This should basically let you do the same portal-through-a-demiplane construction as in Pathfinder, where travelers step into your demiplane through one shadowy door, then arrive at their destination through a second shadowy door.
The problem's that the demiplane only lasts for an hour without an apparent mechanism to make it permanent. "How are spells made permanent in 5e?" has some discussion on this problem.
D&D 3.5e (again): Also walk-through demiplane with permanence issues
In D&D 3.5e, you could create permanent demiplanes using Genesis. And it had permanent planar portals like Pathfinder. The only problem is that there's not something like Create Demiplane, Greater that enabled players to create their own permanent portals, except for the Gate Key.
The epic-level prestige class, Cosmic Descryer, could make the Gate spell last for a few days though:
Enduring Gate (Su)
Starting at 3rd level, as a full-round action, the cosmic descryer can make any casting of the gate spell remain for a full day, rather than disappearing after 1 round per caster level. Every three levels thereafter, the cosmic descryer can increase the duration of gate by one additional day.
But since D&D 3.5e has the Gate Key, that's probably the easier solution.