I believe, like many of the other game effects, they can stack, to a point. Like, you can have natural regen, A spell related regen, and item regen. I'm not sure if 2 regen items stack, but I know the spells say that they don't stack.
Surely, two of the same kind will not stack, but I think that I once tried to stack a 'Hydra Skin Armour' with a 'Ring of Regeneration' and that richt-clicking the regeneration icon showed successful stacking. I am merely wondering if different kinds stack (spell, item, bless & innate).
Spells don't stack. I think it would be cool if they did. Some people have complained about battlefield enhancements not stacking, as it would allow regular units to easily take SCs.