Ricardo Matosinhos has crafted an online survey that lists type of player (professional/amateur/teacher), type of horn, mouthpiece model for a random and limited but interesting comparison of what players are using these days.
Choosing a French horn mouthpiece - articles by Bruce Hembd, Part I (Rim, intro), Part II (cup, throat, bore), Part III (weight, plating, shopping tips)
The Farkas Model Mouthpiece - article by John Ericson on the most classical horn mouthpiece of them all.
Osmun Mouthpiece Catalog (pdf file)
The horn repair shop + accessory emporium of Osmun offers a pdf file with useful information about the mouthpiece ("Designing Your Own Mouthpiece," "Anatomy of a Mouthpiece") and organizes its offerings into "sound families" ("London", "Chicago," "New York," "Vienna").
Lawson Horn Mouthpieces - Walter Lawson on horn mouthpiece design.
Laskey Mouthpieces
Scott
Laskey offers 4 sizes of mouthpiece diameters (17 to
18.5mm), 3 cup sizes, and a "unique rim contour".
Superstar Gail Williams plays an 85GW Laskey horn
mouthpiece.
Moosewood - Custom horn mouthpieces, rims, underparts, + accessories (stem weights, visualizers, left hand supports, etc.). Maker Tom Greer also makes Vienna horn mouthpieces and will make custom mouthpieces to your specifications, and will repair damaged mouthpieces, and silver or goldplate a rim or mouthpiece.
Left to Right: Megamoose, Magnum Opus

Stork - Custom horn (and other brass) mouthpieces.
PHC Mouthpiece System - Paxman/Halstead/Chidell system of 12 rims + 3 finishes + 15 cups => 540 possible combinations. "An imaginative player will select cups to musically enhance particular areas of the horn's repertoire, range, and tone quality, without any unsettling effect on the embouchure."
YouTube video on how a [Taylor trumpet] mouthpiece is made. Irritating accompanying music, but turn the sound off and it's an interesting tour of mouthpiece-making.
Thompson Edition Mouthpieces - a series of mouthpieces designed by David Thompson, solo horn of the Barcelona Symphony; 3 models. Also offered is a unique embouchure visualizer, with a rim identical to the Thompson mouthpieces.
Warburton - mouthpiece specialist
Houser Horn Mouthpieces - used by players in the Philadelphia Orchestra, Metropolitan Opera, etc. Stainless steel rims available.
Patterson Hornworks - Standard model (screw rim; similar to older Chambers model), DeRosa Model (screw rim), Geyer Model (screw rim).
Curry Horn Mouthpieces - precision mouthpieces available in 3 diameters with 2 cup shapes. Custom and delrin-rim mouthpieces available.
Marcinkiewicz Inc. - Pro-line Concert Hall horn mouthpieces
Greg Black - Five basic models of horn mouthpiece, plus their BP model, said to be "the only horn mouthpiece designed for players who wear braces."
Horn Guys - horn mouthpieces made by Mark Atkinson, Scott Laskey, Jim Patterson, Giardinelli, Farkas, Moosewood, Faxx, and Marcinkiewicz. Useful charts and descriptions.
whf -mouthpieces - Austrian maker of mouthpieces for the Vienna horn.
Mouthpiece Comparison Chart
Handy chart by Toru Ikeno that compares the dimensions of the horn mouthpieces by 16 mouthpiece makers.
Mouthpiece Bore Sizes
A chart by Osmun.com correlating bore sizes: decimal with fraction, number, or letter.
Mouthpiece Comparison Chart [#2]
Similar information done using a graphic design - showing models on a continuum. By Best Brass Corporation of Japan.
French horn mouthpiece comparison chart - by wwbw.com. pdf (downloadable) file
Mouthpiece Specification Chart (all brasses) - by Mouthpiece Express
Select up to four (short list of standard mouthpiece makers - but no Holton, no Moosewood, etc.) and see a chart comparing their specifications.
Mouthpiece Manual
Downloadable 35 page pdf file of information on mouthpieces. Discusses all brass and is only about Bach mouthpieces, but worthwhile for the clear explanations and diagrams.
Kelly Mouthpieces
If you have ever needed or wanted a mouthpiece made out of something other than metal (i.e. clear plastic) or a different colored mouthpiece (red, blue, green, black, yellow, etc etc), this is the place to come. Available in medium cup and medium deep cup sizes. $21 each. Kelly also offers care & maintenance items & mouthpiece pouches.
On the other hand, if you fancy Mouthpieces Made of Precious Woods, Maurice Benterfa has designed a number of them (made in Spain by Stomvi-Honiba), using 7 kinds of exotic hardwoods (he doesn't specify which). There is a short discussion of the use of wooden mouthpieces at Hornplayer.net.

French Horn Mouthpiece Repair Tool - fix bent 'ends' of dropped mouthpieces