These are pretty fun. I especially like the theory about Tyrion being part Targaryen.
All the Game of Thrones Fan Theories You Absolutely Need to Know
Who Are Jon Snow's Parents?
It's the question every A Song of Ice and Fire readers asks themselves in book one, and never stops asking. The most prevalent theory is that Prince Rhaegar Targaryen, who abducted Eddard's siter Lyanna and the love of Robert Baratheon's life and inadvertently started the rebellion that deposed the Targaryens, had sex with Lyanna –- maybe consensually, maybe not –- and Lyanna died giving birth to Jon. Knowing that Jon would be in considerable danger if his half-Targaryen blood were revealed (remember, Robert was determined to kjill every last Targaryen on the planet), he pretended the boy was his own bastard, and took him to Winterfell, telling nobody the truth. Although Ned is incredibly secretive regarding Jon's parentage, he does remember making Lyanna a promise on her death bed, which was likely to keep Jon secret and safe.
Jon's parentage seems likely to most readers – so likely, in fact, that some people believe it's too obvious to be true. Other fans have theorized that Jon is genuinely Ned's child, possibly with some random woman, or possibly with Ashara Dayne, whom Ned was rumored to love. The question is whether Ned's honor is great enough to have precluded him from fathering a bastard — certainly Catelyn and Ned's friends were shocked at the idea Ned had cheated –- and as shown in GoT, Ned is honorable to a fault. So it seems unlikely, although if he did lapse, his shame might be the reason he's so quiet about Jon's parentage. But if his mother is Ashara Dayne or some random wench, that doesn't really explain why he wouldn't at least tell Jon.
Certainly, George R.R. Martin loves his head games, but the idea that Rhaegar and Lyanna are Jon';s true parents makes the most narrative sense. And it seems unlikely that Martin would be hinting at the mystery so much only to reveal Jon is just Ned's regular ol' bastard.