For convenience, I've divided the ascending devices in my collection into a number of categories. Although there are more rigorous methods to classify ascending devices, I've chosen an informal approach that I think will be easier for most people to follow than some purely academic method.

Eccentric Cam Ascenders
These are ascenders that pivot on the frame and grip the rope by wedging action only. I subdivided these as follows:
Lever Cam Ascenders
Lever cam ascenders have the climber's weight attached directly to the ascender. For Type 1, the order is rope contact-pivot-sling. I subdivided these into handled ascenders and handleless ascenders. For Type 2, the order is pivot-rope contact-sling.
These are ascenders where the rope passes under a rocker arm and above an anvil. Tension on the standing line rotates the rocker by raising the standing line end of the rocker, pinching the trailing line between the other end of the rocker and the anvil.
Ascenders where the sling rope grips the main rope. These are essentially knots with metal (or other) parts added.
Ascender Knots
Ascenders where the sling rope is tied around the standing rope, and no metal parts are involved.
The famous M.A.D. (Motorized Ascending Device), powered by a gasoline engine.
The ascenders that don't quite fit into the preceding categories.

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.
 Channel Diameter  This is the diameter of the rope channel in millimeters. On most of these ascenders the dimension varies a bit depending on where it is measured.
 Cam Angle  Most eccentric cam ascenders use an equiangular spiral for the shape of the cam, although some use a circular arc and others use more complex patterns (e.g., two spirals). I've given the equivalent cam angle that I measured. I believe this is accurate to within about ±2 degrees.
Tooth Pattern  The tooth pattern is best described by example: (F)(2.H)^2(3.2) would have, starting at the top, a flat area (F), a row of two teeth, a hole (H), another row of two teeth, another hole (the ^2 means the pattern is repeated two times), a row of three teeth and finally a row of 2 teeth. In other patterns, "S" stands for a single longitudinal slot, and "Z" stands for wide "Z"-shaped (not conical) teeth