Any kind of climbing

Ice climbing: Ascending ice or hard snow formations using special equipment designed for the purpose, usually ice axes and crampons. Protective equipment is similar to rock climbing, although protective devices are different (ice screws, snow wedges).
Bouldering: Ascending boulders or small outcrops, often with climbing shoes and a chalk bag or bucket. Usually, instead of using a safety rope from above, injury is avoided using a crash pad (a combination of high and low density foam, within a heavy duty fabric structure, often transported on the back) and a human spotter (to direct a falling climber on to the pad).
Buildering: Climbing urban structures - usually without equipment - avoiding normal means of ascent like stairs and elevators. Aspects of buildering can be seen in the art of movement known as Parkour.
Tree climbing: Ascending trees without harming them, using ropes and other equipment. This is a less competitive activity than rock climbing.
Rope climbing: Climbing a short, thick rope for speed. Not to be confused with roped climbing, as in rock or ice climbing.
Pole climbing (gymnastic): Climbing poles and masts without equipment.
Pole climbing (lumberjack): Lumberjack tree-trimming and competitive tree-trunk or pole climbing for speed using spikes and belts.

Rock, ice, and tree climbing all usually use ropes for safety or for aid. Pole climbing and rope climbing were among the first exercises to be included in the origins of modern gymnastics in the late 18th century and early 19th century.