What's the Deal with Seath the Scaleless?

CrystalBlue's answer provides a good rundown of what we know about Seath in confirmed canon- though I should note that I don't believe it is confirmed that Seath is Priscilla's father. It seems extremely likely and the community tends to take it for granted, but it is not actually confirmed in-game.

EpicNameBro runs down what we know (canon) and suspect (non-canon) about Seath in his Dark Souls Lore series (skip to 3:44):

Essentially, he's one messed up dude, much like most of the Dark Souls cast. It's believed that he betrayed the other dragons because of jealousy, but the nature of his betrayal is unknown- ENB puts forth the idea that Seath stole the Primordial Crystal from the other dragons, which allowed them to be killed by Gwyn and the other Lords. Some believe rather that the crystal was made by Seath in his experiments (though the title 'Primordial' seems to contradict this).

Something that Seath learned in his archives while studying immortality drove him to insanity; the same thing happens to Big Hat Logan if you let him poke around inside the archives enough. Again, this knowledge seems to have something to do with crystals.

It's interesting to note that, at the time you meet him, not only is Seath scaleless and colorless but also sightless and legless. It's unknown which of these mutilations he was born with, and which of them were caused by his research. Personally, I think that he was born with all of them, going mostly off his appearance in the intro cinematic. His body is partially covered with crystals, however, and this is clearly something that happened to him after he started experimenting with them.

On the subject of Priscilla: Again, ENB goes over this in the video, but the main reasons that people believe Seath is Priscilla's father are:

-They're both albino.
-Priscilla lives in the Painted World, a place where forsaken people/objects/magic go. Being the spawn of a dragon (who's pretty freakish himself) and... something else... would definitely make you fall into this category.
-Seath had a thing for capturing maidens. I'll let you fill in the blanks.
-Like you said, there doesn't seem to be many other candidates, especially since Seath is the only dragon known to have lived (at one point peacefully) close to civilization.

If Seath is Priscilla's father, than that makes pretty much any humanoid (not really human, the people of Anor Londo were more like gods) female a candidate. Gwynevere herself is sometimes considered, along with all of the handmaidens of hers that Seath kidnapped.

(Personally, I can't help but wonder if Seath would even be capable of fathering an offspring. He doesn't have any legs, and he's pretty mutated in almost every other way. Eh. Just a thought.)

There is actually a lot of lore on Dark Souls that you can dig up. Most of it comes from items, like it did in Demon's Souls. But here's a quick run-down of Seath The Scaleless.

(http://darksouls.wikia.com/wiki/Seath_the_Scaleless)

Seath was born, as his namesake suggests, scaleless. Because of this, he wasn't granted the same Stone Scales of Immortality and felt anger at the other dragons. Because of this, when Gwyn went to war with the other dragons, he sided with Gwyn to help defeat them. Afterwards, he was named Duke by Lord Gwyn and given his own tower and archives to do magical research. This research, which was to acquire the Scales of Immortality, was fruitless and drove the dragon insane.

He is also considered the grandfather of magic in the world of Dark Souls. He is also the 'father' of the Pisaca, Pricille the Half Breed, and the Moonlight Butterflies.

I find that if you look around, Seath has the largest tangible impact on the game, some of which is speculation, but is pretty valid.

For example, many of the enemies you come across are quite obviously (and some less so) his creations, such as the Crystal Golems, Moonlight Butterfly's, Crystal Hollows, and of course Seath's eyes and ears, the Channellers. Even the Crystal Lizards are believed to be his.

He's at least partially responsible for Havel being locked in that tower. Think about it. Havel hated magic and dragons, and thus would not have liked Seath at all. This would have lead to a shared animosity, considering how well the dragon reacted in the past to being shunned. When Havel was locked in the tower 'for his own good' as one item description says, I believe Seath was responsible for letting him out again when Gwyn returned, and seeing as he never did, Seath never bothered. I like to think that's why the key is found on a Moonlight Butterfly, one of Seath's creations, so that Havel could never escape.

It's pretty much assured, even if never explicitly stated, that Seath is Priscilla's father, though the mother is unknown. However, considering his obsession with kidnapping maidens and performing horrifying experiments on them, perhaps there is no mother, and she is his own attempt at splicing a daughter via magic?

There is a Channeller waiting in the church where Rhea goes to, and shortly after she disappears and ends up in the Archives, hollow. This is obviously his doing, direct or not. It's also possible the Channeller is why Lautrec is locked away.

He's obviously completely mad, considering what he's done to himself. Being born albino with no scales, no legs, thin insect wings, possibly no eyesight and no immortality drove him to research ways of obtaining said immortality. His jealously over his fellow dragons having their scales is what drove him to betray them to Gwyn and is implied to be the a big factor in how they won. His obsession with immortality moved him to the crystals, and this could have lead to several things happening, including the crystalification of many creatures and things, such as perhaps the Crystal Knight, and all the Crystal weaponry that can be found. Crystallising himself partially may have been what he did before he learned of the Primordial Crystal.

And of course, we can't forget that he was the grandfather of sorcery, and thus has an indirect hand in every spell you or anyone else casts. Which brings me to Logan, who goes just as mad as Seath does, and even sheds his clothing to try and imitate the white beast. Seath's obsession with crystals as well as his affinity for magic may be where curses come from.

I like to think, with his penchant for kidnapping maidens and experimenting on them, his creation of countless horrors, including his 'new and improved self', and his apparent chronic backstabbing disorder, Seath is one of, if not the worst character in the game. He is a complete monster who chose to do most of what he did before he went mad, and even after that it continued, horror after horror. It brings me a cold satisfaction for me to kill such a sick creature.