Another important point that's gotten little attention so far in this thread is that the risk varies greatly from one substance to another. Some component chemicals, such as sodium carbonate, are common household chemicals used for other purposes (as a laundry booster, in the case of sodium carbonate). A few, such as ascorbic acid (vitamin C) may even be ingested (although of course there's a lethal dose even of such chemicals). Of course, being a common household chemical doesn't mean it isn't risk-free -- sodium hydroxide (lye) is often used as a drain opener, but the fact that it's a common household chemical doesn't mean you should be careless in its use, in or out of the darkroom.
As for cacinogenic effects specifically, I haven't seen warnings about this for most photochemicals. One exception that springs to mind is formaldehyde, which is used in C-41 stabilizer (but not in the newer C-41 final rinse). My reading of the issue is that the studies of formaldehyde's effects on humans produce mixed results, and those that show effects are studies in which subjects receive huge doses. Thus, for C-41 stabilizer, it's probably adequate to just wear gloves, so long as you're not doing massive quantities of C-41 processing.
I'm certain there are other photochemicals that are known or suspected carcinogens, but I don't recall the details. They're relatively uncommon, though.
