The other two answers list the people who are alive and could possibly have knowledge of Jon's parentage. I.e.
- Howland Reed
- Barristan "the bold" Selmy
And (ADWD spoilers)
- Jon Connington
- Septa Lemore aka Ashara Dayne
Also to be included in the list is of course Howland Reed's children, Jojen and Meera. They did in fact come close to the topic of Rhaegar and Lyanna when they told Bran of the story of the Knight of the Laughing Tree. So close, in fact, that I half expected they were about to reveal something to Bran.
However, there is another option, stemming from the prophecy that Daenerys got in the House of the Undying:
Her silver was trotting through the grass, to a darkling stream beneath a sea of stars. A corpse stood at the prow of a ship, eyes bright on his dead face, gray lips smiling sadly. A blue flower grew from a chink in a wall of ice, and filled the air with sweetness...mother of dragons...bride of death..
The blue rose is no doubt a reference to Lyanna, as she was notably fond of such. The wall of ice is of course The Wall. And the context in which this is mentioned is "bride of death", where the first mentioned "husband" is presumably Drogo and the second presumably Victarion. It is fairly reasonable to assume that the third one refers to Jon, since he is presumably Rhaegar and Lyanna's son, and a Targaryen by blood (viable husband), at the Wall, and as of ADWD also (spoiler)
dead (bride of death)
So, while it is not clear exactly how it will happen, it seems this prophecy indicates that Daenerys will meet Jon at the Wall and his parentage will be revealed somehow. All this is, of course, pure guesswork.
There is also the option which will be completely covered by spoiler tags, since it mainly takes place in ADWD:
Bran is now a greenseer and an apprentice of Bloodraven. He has already seen Ned Stark with (presumably) Jon and Robb, praying before the heart tree "Let them grow up as brothers". I think it is probably very likely that Bran will look deeper into history there and find out the truth about Jon.
Bloodraven himself will also have a lot of knowledge about house Stark, as he has been watching them for years. And it is not unlikely that he will have paid close attention to the events surrounding Rhaegar and Lyanna.
Also, it is likely (or perhaps only possible) that Coldhands is in fact Benjen Stark, who might have knowledge of Jon's parentage.
I think it is interesting to note, however, that (ADWD spoiler)
...GRRM drops quite a few hints that Jon is actually the son of Ned Stark and a fisherman's daughter. Firstly, it is mentioned in a Davos chapter by the Lord of Sisterton regarding Ned Stark and a fisherman's daughter that "he left her with a bastard in her belly and a bag of silver" (paraphrasing). Secondly, Stannis says "You haggle like a crone with a codfish, Lord Snow. Did Ned Stark father you on some fishwife?" And Jon himself thinks something like "Perhaps he did, at that"
Although a possibility, I am more inclined to think this is a red herring, however.