Which rare drops can drop already enchanted?

The only items that can be enchanted are Golden Swords from Zombie Pigmen and Bows from Skeletons.

The swords, if enchanted, have their enchantment chosen randomly as if it were a level 5 enchantment from an enchanting table. The following enchantments are therefore possible:

Sharpness I–III
Smite I–IV
Bane of Arthropods I–IV
Knockback I–II
Fire Aspect I–II
Looting I–II

Bows, if enchanted, will always have Power I.

Thanks for being concerned about sources! I was involved in writing the wiki page on rare drops, which we did based on this decompiled source code. I cannot vouch for that code being the actual code in Minecraft (especially as it may change in the future), but what it indicates is this:

First, whether the drops are enchanted is chosen, with 20% chance modified by Looting.

Then, the item to drop is chosen depending on the above choice. That is: If a Zombie Pigman passes the chance to get rare drops, and the chance to get enchanted rare drops, then the item will always be a golden sword. If the item is not to be enchanted, then you get an equal chance of all three possible drops.

I don't have the code for zombies, so I can't say exactly what their drops are set up to be, but no one has ever reported enchanted armor, so I assume it does not happen. Skeletons of course only drop (possibly enchanted) bows.