Abseiling

Knee-pads (and sometimes elbow-pads) are popular in some applications for the protection of joints during crawls or hits. Wikipedia]

Boots or other sturdy footwear with good grips may be worn, especially climbing shoes. [Wikipedia]

Gloves protect hands from the rope and from hits with the wall. They are mainly used by recreational abseilers, industrial access practitioners, adventure racers and military as opposed to climbers or mountaineers. In fact, they can increase the risk of accident by becoming caught in the descender in certain situations. [Wikipedia]

Helmets may be worn to protect the head from bumps and falling rocks. A light source may be mounted on the helmet in order to keep the hands free in unlit areas. [Wikipedia]

A prusik, Klemheist knot, or autoblock knot may be used as safety back-up, commonly referred to as an 'autoblock,' and is used as a back-up in the case of the abseiler losing control of the abseil. One of these friction hitches is wrapped around the rope below the rappel device, using a short loop of smaller diameter cord or webbing, often called a 'prusik loop'. The prusik loop is then attached to the belay loop or leg loop of the harness. [Wikipedia]

A climbing harness is often used around the waist to secure the descender. A comfortable climbing harness is important for descents that may take many hours.[Wikipedia]

A descender or rappel device is a friction device or friction hitch that allows rope to be payed out in a controlled fashion, under load, with a minimal effort by the person controlling it. The speed at which the abseiler descends is controlled by applying greater or lesser force on the rope below the device or altering the angle at which the rope exits the device. Descenders can be task-designed or improvised from other equipment.

Anchors for abseiling are sometimes made with trees or boulders, using webbing and cordellete, or also with rock climbing equipment, such as nuts, hexes and spring-loaded camming devices. Some climbing areas have fixed anchors such as bolts or pitons for rappelling off of without having to leave other (more valuable) gear behind. [Wikipedia]

Ropes: Climbers often simply use their climbing ropes for abseiling. For many other applications, low-stretch rope (typically ~2% stretch when under the load of a typical bodyweight) called static rope is used to reduce bouncing and to allow easier ascending of the rope. [Wikipedia]