For convenience, I've divided the rappelling (a.k.a. abseiling) devices in my collection into a number of categories. Although there are more rigorous methods to classify rappelling (abseiling) devices, I've chosen an informal approach that I think will be easier for most people to follow than some purely academic method. The categories are loosely defined as follows:

The rope follows an "S" path around two bollards. True bobbins have the center of each bollard fixed to the frame. They come in plain and stop versions. False bobbins have bollards whose centers move with respect to the frame.
Carabiner Methods
Rappels using carabiners only or carabiners and brake bars only.
Figure Eights
Devices that look like an "8." Deaf eights don't have ears; obviously eights with ears do. There are complex eights with moving parts, and toy eights that are not intended for rappelling.
Fixed Multi-bar Devices
The rope snakes around at least three bollards, all of which are fixed.
An ill-defined catch-all category, but generally the rope wraps around a rod.
Another ill-defined "catch-all" category for devices with horns or prongs.
Poly-bollards (the best name I could think of)
The rope snakes around at least three bollards, at least one of which moves to provide a stop function (other wise, I'd call it a Fixed Multi-bar Device).
Devices with frames that accept a number of brake bars, at least some of which can move on the frame. J-frame racks have an open side, U-frame racks do not.
Devices where the rope wraps around a drum. The drum axis can be horizontal or vertical.
Lever Boxes
Devices with an enclosed rope channel and a control lever.
All the rest.

A word on the tables…

The tables include some numerical data:

 ID  This is just my catalog number so that I can keep these straight.
 Weight  Weights are in grams. Webbing, slings, etc. are not included.
 Height, Width, Thickness  I've given the dimensions in millimeters. The measurements are in perpendicular directions. I've chosen to measure the maximum dimensions instead of the most obvious dimensions. Sometimes this leads to numbers that are more than what you would expect - for example, the thickness of a bent plate would be more than the thickness of the unbent plate.
Standard Volume   The standard volume is just the product of the height, width, and thickness divided by 1000. This gives a volume in milliliters of a box that the device will fit into. Odd shaped devices are penalized by this formula, but since they are generally harder to pack, this number might be useful.