The Opusculus Lamae Bal ta Mezzamortie tells of how the curse of vampirism came about, owing its creation to the Daedric Prince Molag Bal. The tale goes that Molag Bal disliked Arkay, an Aedra who showed great pride in his sphere (the cycle of life and death). So Molag Bal traveled to Tamriel (still newly-formed at the time), where he savagely raped the Nedic woman Lamae Beolfag and departed Nirn. Lamae was found and nursed by nomads, but death eventually overtook her. On the night of her cremation, she rose again, and brutally murdered the nomads. Dubbed a Daughter of Coldharbour‎, she then created more vampires, spreading the curse across Tamriel and making a mockery of Arkay's cycles.
In actuality, Lamae did not die at all but was rapidly healing from her wounds which frightened the local nedes, and in fear of the disease that was spreading through Lamae, they tried to cremate her but she awoke and slaughtered them all, after having coming to her senses and being horrified of which she did and what she became, she beseeched Arkay only for him to apparently forsake her, in retaliation, she began spreading vampirism to the followers of Arkay. Since then, many mortals have made pacts with Molog Bal to become vampires, given rise to new bloodlines of vampires, each with their unique gifts but sharing some. Harkon and his family being such a case as they are responsible for the Volkihar bloodline, a bloodline nearly as old as Lamae's.
This account has variations in Temple doctrine, with Molag Bal spawning the first vampire from a defeated foe, such as a Daedra Lord, a Temple Saint, or a "powerful beast creature". Indeed, multiple origin stories may have truth to them, as in the case of the Volkihar vampires of Skyrim, who descend from a single family that were given their abilities from Molag Bal directly. These multiple 'first' vampires may be the source of the different bloodlines of vampire clans, which have unique abilities and characteristics.
The association of vampirism with Molag Bal may be one reason the Mace of Molag Mal, which allows the bearer to absorb an enemy's magicka, is also called the Vampire's Mace. Of course, anything which absorbs power from a victim is often associated with vampires, such as the strength-sapping Vampiric Cloud spell, the Ebony Blade (also called the Vampire), and the Vampiric Ring.