Bleach in drain cleaners
Lye is very corrosive, just like acid, except opposite (hope that makes sense). Although lye is a very powerful chemical, and it is sufficient for many blockages, oxidizing agents (like bleach) may be helpful for breaking down paper/cellulose blockages.

Mixing bleach with acid will cause chlorine gas evolution... bad, bad, bad.

EDIT- The oxidative powers of hypochlorous acid and hypochlorite ion(s) compared:



Source: Descriptive Inorganic Chemistry, Third Edition (By Geoff Rayner-Canham, Tina Overton)

So in terms of power, yes hypochlorous acid is a stronger oxidizer, but it's not wildly different. 

On a related note (see comments below) hypochlorous acid is a much better microbicide than the hypochlorite ion, because it penetrates cell walls more easily. However, regarding a drain cleaner, the oxidative difference is much less pronounced. And it's worth mentioning that at above pH 12, a cell will lyse (burst open) and become saponified, so that obviates whatever microbial effect hypochlorite or hypochlorous acid might have on bacteria... like being thrown into a poisonous wood chipper.