Yes, they do. Although some individuals have brownish or pink skin (just like humans have variations in skin colour). Their stripes come from a pattern of white hairs on their coats. And no two zebras have the same stripe pattern– it’s like a fingerprint!
Just to clarify, zebras have dark skin but the black stripes you see are actually black fur (not the skin itself) and of course the white stripes are white fur. Also keep in mind that there are three zebra species and they have some slight differences in their stripes. For example, some have narrower stripes and some have broader stripes, and one of these species has some gray-ish fur in addition to the black and white stripes.
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James commented on :
Answer: Tigers have stripy skin!