A trio of researchers at Korea Advanced Institute of Science and Technology, working with a colleague at the University of Illinois at Urbana-Champaign, has designed and built a working quadruped robot with magnetized feet that can climb on the walls and ceilings of metal buildings and structures...

The robot was uses both magnetic elastomers and electro magnets. Together, they allow the robot feet to magnetize and demagnetize on demand. By turning the magnetism on and off, the robot is able to have a single foot cling to a vertical spot on a wall and hold on while other feet are adhered—and then to let go with one foot at a time to take steps.

The researchers also had to program the robot to allow for first beginning a climb and then for moving around or over obstacles. For this, they simulated the way a cat tests a surface before moving forward, taking tiny first steps with its front paws before adding the action of back paws.

Testing showed the robot capable of climbing metal walls and walking across ceilings in their test lab. Further testing showed the robot was able to climb up an old outdoor storage tank with walls orange with rust.

(Via TechXplore)

Of course, science fiction authors have been keen on the idea of magnetic boots for at least the last three generations. Here's a quote from Atomic Fire (1931) by Raymond Z. Gallun, the earliest reference I know about:

Aggar Ho smiled sadly. "Perhaps," he said, and then, after a pause, "Thank you, my boy." He tramped wearily up the spiral stairs, his magnetic boots which served to hold him to the steel floor in the absence of gravity making a clattering noise.
(Read more about magnetic boots)

Jack Williamson makes great use of this idea in his splendid 1933 classic Salvage in Space:

His "planet" was the smallest in the solar system, and the loneliest, Thad Allen was thinking, as he straightened wearily in the huge, bulging, inflated fabric of his Osprey space armor. Walking awkwardly in the magnetic boots that held him to the black mass of meteoric iron, he mounted a projection and stood motionless, staring moodily away through the vision panels of his bulky helmet into the dark mystery of the void.

('Salvage in Space')