While some games allow characters to climb up walls or cling to them, this details games where characters can walk or run along or up walls and significant slopes.
There are two general ways in which games contextualise this ability. In brief, a resource based limitation for the skill or a somewhat permanent availability.
The former example has characters depend on moving quickly without collisions, saving energy or avoiding other limitations to continue. These cases may be bound to the acrobatic ability of the characters involved like in the majority of Sonic the Hedgehog platformers due to how shuttle loops and slopes into walls are recurring elements.
The latter example tends to reserve itself to select surfaces or conditions like ones needing magnetic boots or Bayonetta's ability to stand and perform basically all actions on walls when the moon is out.
There are also cases of both being used together with Spider-Man in Spider-Man 2 being able to run and slide on walls in all directions including downwards, but players can also stick to walls to wall crawl more slowly but also perform some actions and attacks.
Jumping off walls is a common supplementary mechanic regardless.
Development of 2003's trendsetting Prince of Persia: Sands of Time was influenced by the Tony Hawk Franchise.