Do the effects of rings stack?
Yes. It does stack. Member of wiki discovered. Search in-page for word stack and you will see: http://pixeldungeon.wikia.com/wiki/Thread:3013
Rings appear to stack (besides ring of haggler)...
With two rings of mending + 2, natural regeneration is more than doubled. Without the two rings, the hp regen appears to be +1 per 10 ticks (wait actions). With 1 ring the hp regen is +1/7 ish, and with 2 rings, the hp regen is a little faster than +1/5. The rings appear to have no effect when starving.