Reading through this thread, I notice that several people have problems with their chamfer planes; I also notice that some of these planes have Rube Goldberg-like mechanisms that remind of metal multi-planes in their ungainliness. Here's a suggestion: chuck your chamfer plane in a dusty drawer, and plane to a pair of lines with whatever bench plane you like. You will never have the sort of problems with the depth mechanism that Derek and Patrick described, if there is no depth mechanism. Draw two lines and don't go past them, and your chamfers will be perfect, or perfect enough.
Aside from the issues already mentioned, chamfer planes have a lot of limitations. There are a lot of chamfers in woodworking that aren't 45°; for example if I am chamfering the underside of the ends of a tabletop, the chamfers will be a lot shallower than 45°. An ordinary plane can make any chamfer, but a chamfer plane can only make one. A chamfer plane isn't much help on curves, but any small plane will work just fine for chamfering gentle convex curves.
Not to mention, learning to plane to lines is a valuable skill that will pay off in lots of other applications.
I guess I can see using a chamfer plane if you were making dozens or hundreds of picture frames, and you wanted them to all be exactly the same, without having to pre-mark them. But for most applications, they're really unnecessary.
I suppose the example I gave (of planing hundreds of picture frames or whatever) is how chamfer planes originated, at least in the West. You definitely don't find them in 18th c. tool kits; they show up in the 19th century, when people were doing production work in factories but not yet using power tools for everything. The advantage of a chamfer plane in that situation is that you can hand it to a relatively unskilled worker and set them to work. That's the sort of situation that these planes were made for.
"For me, chairs and chairmaking are a means to an end. My real goal is to spend my days in a quiet, dustless shop doing hand work on an object that is beautiful, useful and fun to make." --Peter Galbert