Death was once seen in many different guises, according to the beliefs of the deceased, hence he appeared as a giant scarab beetle to the pharoahs. However, Death decided not to bother any longer, and now appears in the almost universally recognised costume of a giant skeleton, with a scythe and a hooded cloak.
The Death of the Discworld is unusual in that, as humans eventually come to resemble the dogs that they own, so he has come to resemble slightly humans. He has been known to prevent people from dying (though not often - don't assume he'll do that for you) and adopted a girl called Ysabel.
He also later took on an apprentice called Mort and he eventually married Ysabel (Mort that is, not Death) and became Duke of Sto Helit (after an unfortunate incident involving teenage lust and general stupidness).
They had a child called Susan, who refers to Death as 'grandfather' and has taken his responsibilities on on occasion when he has been absent and has strange abilities as well as a mark on her face from when Death hit her father.
Which just goes to show that DNA knows nothing.