This page was inspired by the discussion on the (now-defunct) Canon EOS mailing list in November 1996 regarding whether the the EOS shutter speeds are stepless. Not long ago, the same question was asked about the aperture values.
I performed some observations in November 1996, and here are the results. The short answer is: no, they are not stepless. But the step is quite small.
Method: Removed film from camera, opened the back and pushed in the small lever which tells the camera that the back is open. Now the operation of the aperture can be observed when the shutter is open for exposure. The camera with the 28-105 mm lens was mounted on a tripod and pointed at a brightly lit corner of the room. Tv mode, with the shutter speed of 1/3 seconds and continuous drive were selected. AF was turned off. Film speed was adjusted to obtain a reading of f/5.6 at 1/3 sec. Averaging metering pattern was used.
I kept the shutter button depressed, and moved my hand in front of the lens while observing through the film window during the time when the shutter was open. The camera takes a new reading before each exposure, opening the aperture more and more as my hand blocked more of the light.
I could observe 5 or 6 discrete steps between the 5.6 (displayed) and 3.5 (wide open) aperture values. I could miss some due to vignetting close to the wide open position, or by moving my hand too fast. The max. aperture could also be slightly diferent from 3.5 (and the camera may know this). But there are no doubt quite visible discrete steps. My current guess is that the aperture is settable in 1/6 step increments (allowing for both the 1/2 step settings on most of the bodies, and for the 1/3 step settings on the EOS 1n).
Generalizations: the above is true for the lens I used (Canon 28-105mm f/3.5-4.5 USM). There is good chance that all lenses behave in a similar way, but I cannot verify that.
Note added on 07-July-1999. Canon has revealed that the light metering system of all EOS cameras uses 1/8-stop steps internally. While it has not been explicitly stated, it may be assumed that the lens also use 1/8 step stops or multiples of these.
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