I make no claim to the legitimacy nor ludicrousness of any of these concepts regarding Jon's conception... I'm just listing what I've read... or think I remember.
Eddard+Ashara=Jon... Eddard's marriage broke his and Ashara's hearts.
Eddard+Wylla=Jon... Eddard broke his marriage vow once... just the once.
Benjen+unknown=Jon... Ben was a wild youth.
Rhaegar+Lyanna=Jon... this is the most popular theory.
Robert+Lyanna=Jon... Ned's promise is to keep Jon from being like Robert... thus the naming after Arryn.
Eddard+Lyanna=Jon... sick.
Benjen+Lyanna=Jon... still sick.
Brandon+Lyanna=Jon... tries to explain why Brandon forsook his bride for Lyanna.
Rickard+Lyanna=Jon... completely sick.
Aerys+Lyanna=Jon... maybe Rhaegar was covering for his old man.
Howland+Lyanna=Jon... helps explain Jon's powers.
Brynden Tully+Lyanna=Jon... trying to explain Hoster's animosity towards Brynden.
Randyll Tarly+Lyanna=Jon... this would mean that Jon and Sam actually are brothers.
The following links may include some origins for Jon that I've neglected.
Spoilers: Theory on Jon
Pure Speculation RE: A Song of Ice and Fire
"promise me, Ned" and "the value of Howland Reed"
spoiler: knight of the laughing tree = Jon
Spoilers: A new theory on Jon
Jon Snow
About the only other thing that has not been mentioned is the possibility of an immaculate conception.
KESpires, you are an evil, evil man for dredging this back up... I love it.