Thinking Up Portals

In science fiction, fantasy, and superhero stories, many times a character will need to get somewhere else in a hurry. And obviously, there are few ways faster than teleportation. But simply appearing can lack a certain...pizzazz. That stepping out of a hole in the air can certainly grant, all the more so if you generated it yourself.

This trope involves characters who can create a portal using their superpowers or magical powers, or by having personal portal-generating equipment added as part of a Cyborg Upgrade. Note that if the portal isn't the sort that requires you to step or jump into it, it probably isn't this trope, and if it requires any external equipment, it's likely part of a Portal Network instead.

The name is derived from the "Thinking With Portals" tagline of the Portal video games.

Examples of Thinking Up Portals include:

Anime and Manga

In Digimon, the extremely powerful but rarely-appearing Magna Angemon has "Gate of Density" as his primary attack. It can send enemies through a portal into another dimesion, and lock them there permanantly.

Comic Books

Marvel Comics characters Doorman and Spot have portal-based teleportation as their powers, while villain Black Hole, a "living singularity", could suck objects through a portal in his body to another dimension.
In the New Universe Psi-Force series, Sedara Bakut can create door-like portals in space.

Fan Works

Doug Sangnoir of the Drunkard's Walk fanfic cycle has demonstrated the ability to generate portals, albeit at a kind of remove -- he manifests a simulacrum of a team member who has the power to do so, as seen in an early chapter of Drunkard's Walk VIII.

Tabletop Games

In Scion, characters who learn Boons from the Psychopomp purview can do this: Rainbow Bridge (Psychopomp 7) lets a character teleport anywhere in the World, and Otherworldly Portal (Psychopomp 9) allows a character to teleport between planes of existence.

Video Games

Kingdom Hearts: Corridors of Darkness can be opened by anybody who gets too close to the Darkness.
The Shifters in The Longest Journey can open portals to Arcadia at will.
Touhou: Yukari Yakumo is known for her "gaps", and actually sits on one in her portrait.
Teleportation spells in The Witcher appear to work in this fashion.
This is pretty much what Portal and Portal 2 are all about, the only deviations being that it's a gun that's making the portals, and you need a certain type of conductive surface to hold them.
Prey's Hunters and Harvesters travel around the Sphere via portals that the Mother creates for them; it's very usual for you hear the familiar hissing sound their gates make, and seconds later find yourself ambushed from all sides. The Keepers, being higher up in the hierarchy, can use their cybernetics or Psychic Powers to jump around you mid-battle.
In Absorption, though you can't create portals, you need to replace existing ones to solve puzzles.

Webcomics

Desdemona in Evil Inc. can manifest portals for traveling through - completely or partly, or simply for slipping other things through (and even holding them open while ropes pushed through are manipulated on the other side).
Drake in Gold Coin Comics has the power to conjure a teleportation portal.
Fiends in Order of the Stick can travel between planes through portals.

Web Original

In the Whateley Universe, Gateway has found out she has this power. She has been able to summon beings from other dimensions, like Rythax, and also things like fire elementals. And she's learned it's a really fun power to abuse.

Western Animation

In Danny Phantom, Wulf the ghost can create portals to the Ghost Zone at will. Danny's evil alternate-future self can do the same.
As an Eliatrope, Yugo from Wakfu can create teleportation portals. Shushu king Rushu is particularly interested in acquiring Yugo since Eliatrope portals are the only means of travel off the Shushu world.
Breach from Generator Rex can create portals to and from anywhere she wants as long as she can move her giant second set of arms. Though, she can apparently do it by instinct without them.
In Adventure Time, the Door Lords can throw magical keys at any spot they choose, and it will create a door between that spot and wherever they choose to go. The doors can apparently be in any position or angle they want.