Orochimaru has pale white skin and purple skin around his eyes. His eyes are also similar to that of snakes. Does it signify that he belongs to a particular clan? Or is he one of a kind?
In support of @Quikstryke answer, allow me to elaborate more on this topic.
How Orochimaru gained snake-like characteristics
From Orochimaru article on Naruto Wiki:
Orochimaru was an orphan who became a pupil of Hiruzen Sarutobi alongside Jiraiya and Tsunade. Compared to the more laid back Jiraiya, Orochimaru stood out as a genius — his talents, knowledge, and determination were considered by Hiruzen to be that of a prodigy seen once in a generation. According to Tsunade, Orochimaru had a twisted personality even as a child. His sadistic attitude was presumably due to the death of his parents. At some point after losing them, Orochimaru found a white snake near his parents' grave, with Hiruzen's explanation of it representing fortune and rebirth inspiring Orochimaru to study kinjutsu and obtain knowledge of all techniques. Jiraiya theorised that Orochimaru went down this path in an attempt to forget his painful memories.
From the link above, we learn that Orochimaru did not get his snake like eyes from childbirth, but through his research on the white snake that he found near his parents grave. He spent his life researching about immortality and rebirth.
From Orochimaru article on Wikipedia:
Through his experimentations he has also been able to add some snake-like characteristics to his own body
Orchimaru's Snake Techniques
Below is the list of Orochimaru's snake related techniques.
Orochimaru's trademark trait is his affinity with snakes, in addition to impacting the appearance and composition of his true form, and granting him the ability to extend his limbs to abnormal lengths and to take on snake-like traits in battle, caused him to learn a number of snake-related abilities, including learning Sage Mode. His snake-related techniques have been referred to as Power of the White Snake. One such ability is being able to summon giant snakes to fight alongside him in battle, made possible by the summoning contract tattooed on his arm. This allows him to summon snakes within his vicinity, as opposed to having to place his hand on a surface.
If need be, Orochimaru can morph into a giant snake, despite being slightly smaller in size to his larger ones. His signature summon was Manda, a colossal snake which was described as the largest in the world, with immense fighting capabilities. With Hidden Shadow Snake Hands, Orochimaru can instantly call forth snakes from his sleeves and mouth to attack his opponents in large numbers with venomous bites. A stronger variation of this technique was the Many Hidden Shadow Snake Hands, in which the summoned snakes grow noticeably in both numbers and size.
Another usage of snakes comes in the form of his signature weapon, the Sword of Kusanagi, the Kusanagi of Japanese legend. The sword, kept within the mouth of a snake within his own throat, is able to extend to great lengths to attack enemies that are very far away, can be controlled remotely by Orochimaru, and can return to him by turning in a snake. Although he is capable of wielding the sword normally with great proficiency, it's not uncommon for him to use it without ever removing it from his mouth. The sword is stated to be able to cut through almost anything, and despite failing to penetrate four-tailed Naruto's chakra shroud, did push him back an incredible length. In the anime, he is also capable of having numerous Kusanagi-like blades sprout from the mouths of the snakes he summons.
He is also able to summon use one of his larger snakes around its target, trapping it in its stomach. Following this, Orochimaru can speed up the digestion process on the target. His strongest technique is the Eight Branches Technique, which allows him to transform into an eight-headed, eight-tailed giant serpent bigger than the already colossal Manda, another reference to the Japanese myth. This was described as the ultimate snake-related technique, which turned the user into an immensely powerful "Dragon God".
There is never any mention of this in the story so far. The thing that was confirmed was he is an orphan and his parents death influenced him greatly. He also tried to forget their deaths and probably them in general since it was too painful, so he probably dropped usage of his clan name for that purpose. He is considered to be a prodigy, however no mention of any blood limits were mentioned (though not all prodigies need blood limits, ex: Yellow Flash or Hiruzen)
There's no evidence he was born with the snake like markings, but since we see him as six years old in team Hiruzen, it's safe to say he was. A six year old can not experiment on himself darlings xD and I doubt his parents or any other external force experimented on him. sure the purple markings could have been tattoo'd on when he was younger (which is unlikely since they grow with him), but they couldn't have given him snake like eyes. Also, as we see, Sasuke's natural affinity was hawks, yet he summoned snakes. Thus, one can have an affinity and choose something different. It was still a choice, even if it was a guided one ;)
He is clearly of an unnamed clan of some sort. We know Tsunade was of the Senju but it is never named for Jiraiya or Orochimaru. The only source that names Orochimaru an orphan or tells a story of a white snake that I've come across is the wiki mentioned in the current highly rated answer - its own source is from the fight between Orochimaru and the Third where there is a flashback. No mention is made of those facts - but he clearly has the snake-like features back then, before he could experiment.
Much like the Inuzuka, who have developed dog-like features, it would follow that these features came from a clan who dealt closely with snakes in some way and the power of the chakra gave them snake-like features over time.
If there is something valid that mentions the white snake thing in a valid source, that would still make perfect sense with him being in a snake-based clan. Likely, he did develop more snake-like features as time went on, through experimentation, but it is clear that the foundation for this was already set through lineage.
Orochimaru was an homage to a much older story from feudal Japan; his clan was unimportant to the story, so we have no name for it.