If I can throw in some w-a-g figures (haven't googled, happy to hear more accurate numbers!), I'd take a stab that the contraction/dilation of the pupil gives around 5-6 f-stops worth, that when added to the retinas natural *instantaneous* range will give a total of about 9-12 f-stops range for normal, single scene viewing.
But if you then add the time for chemical adjustment - eg night adaptation and vice versa - I'm pretty sure it's up around 22 - 24 stops overall dynamic range. Obviously that figure does not apply to a single scene, but covers the sort of range it has in total, given time to adjust and provided no stray light affects the adaptation (which is the problem on the Moon).
Interestingly, although it's impossible to compare eyes to cameras in a fair way, a good quality DSLR will also give about 9-12 stops of dynamic range for a given single scene.. and of course you can then tweak it and do various 'cheats' (change ISO and use Dark Frame Subtraction, use very large aperture lenses, use High Dynamic Range or Dynamic Range Optimisation, etc to also cover well over 22 stops ..
Smaller sensor cameras may only be closer to half that.