One
of the best methods for belaying with climbing ropes doesn't require
any additional device at all. The Munter Hitch was chosen as the
U.I.A.A. method of choice ages ago, and is still considered to
be an excellent method. For many years I avoided it because it
has nylon running on nylon, but I now use it at times. It doesn't
work as well on stiff caving rope as it does on climbing line,
but then again, those ropes shouldn't be used for belaying any
lead climbs.
The Munter Hitch should be rigged as shown in the main figure, so that the load is on the spine side of the carabiner. Of course, you should use a locking carabiner (preferably HMS type). The Munter Hitch tends to "walk" to one side of the carabiner; placing the load on the spine side causes it to walk toward the spine (replacing the carabiner ist ah Edelrid Frog avoids the issue). The Munter Hitch can be inverted to feed rope in the other direction, in which case it takes on the form shown in the small figure to the right.
Anyone using a Munter Hitch for belay should make sure they know the Munter-Mule combination. I won't go into the details here because this is something on which one should get proper instruction.
The Munter Hitch can also be used as an emergency rappelling
rig, although there are better carabiner
rappel options available.