I was told Jon Snow isn't actually a Stark bastard, but a Targaryon (sp?) bastard. How long before this bit of knowledge is exposed in the show?

I hate to disappoint but there is no such confirmation in the book. A lot of people think it's the case but it is never explicitly stated. It may be completely incorrect and never happen.

I see. Well that is fantastic because here I was thinking I'd had something spoiled, and now I find out I didn't. It does make sense if its true though, since Ned was supposed to be such an honorable man, and he was so defensive with Catelyn when whe asked him about Jon's mother. Anyways, thanks for clearing that up for me.

just one more question, when you say a lot of people think that, do you mean fans reading the books, or the people of westeros?

never mind, avoid the spoilers!

I will only say that he did mean book readers think this theory, not the people of Westeros. If it is true, only one or two people in Westeros would know it.

dammit man. Are the starks targaryons?
If Jon was the mad king's bastard, stanis would probably know, and I bet the blind meister at the wall seemed to know something about him. I can't think of anyone else that might know.

So I think most knowledgeable readers believe that Jon Snow is the son of Rhaegar Targaryn (NOT the mad king) and Lyanna Stark (Ned's dead sister, the one that Robert went to war over losing after Rhaegar kidnapped her).

The books say something about her dying in bed with alot of blood, and her making Ned make a promise. Then you have the fact that he would never admit who the mother was, and Ned being an incredibly, ridiculously, absurdly straight arrow. All that tends to add up to Jon Snow NOT being Ned's bastard, but rather Rhaegar's.

And would make Jon Snow Dany's nephew (as the son of her brother).

I tend to agree, but of all the theories I've seen out there, I think the Jon Snow one is far and away the best. Waaay too many hints about it to ignore.

Here's the description of the whole thing on Wikipedia:

"Only Ned and his bannerman Howland Reed survived the ensuing battle. Ned found Lyanna inside the tower in a "bed of blood", dying. When Eddard recalls the conflict in a dream, there is an additional detail. While the combatants clash, Lyanna screams. The dream then switches to a storm of blue rose petals, blowing across a blood-streaked sky. It is uncertain if these details are accurate memories.[28]

Lyanna died in a room that smelled of "blood and roses". A fever had taken her strength. Her voice had been faint as a whisper. There was fear in her eyes, while she called for "Ned" to promise her something. When her brother gave his word, the fear left her. She smiled, and her fingers clutched his own in a tight grip. They were still holding each other as she "gave up her hold on life". Rose petals slipped from her palm, dead and black. Later, Howland Reed found Eddard still holding the corpse. Howland managed to separate the hands of the living man and the dying girl, though Eddard had no recollection of what happened after Lyanna died.[7] Shortly before her death, Lyanna extracted a promise from Ned.[10] Neither the content of the promise nor the cause of her death are currently known. Her final words were a phrase that would haunt her brother for the rest of his life:

“ Promise me, Ned.[7] ”

wouldn't he be Dany's cousin, or is Rhaegar Dany's older brother and different than the brother we met in season 1?