The primary purpose of a mountaineering or climbing helmet is to provide protection against falling rocks. It is important that both the climber and the belayer each wear a helmet.
Climbers frequently look for a helmet that is compatible with headlamps, especially if the are climbing multipitch routes. A climbing helmet should fit snugly so it won't slip or move as you move, but it should not fit so tight as to cause any kind of discomfort.
The following are the most popular climbing helmets as indicated by GearBuyer.com.