I think just about everyone's heard that theory
I actually think it could possibly be; though, if GRRM's original plan was to do that, he may well have changed it to be less predictable. To me, R+L=J seems pretty feasible; for one, Ned never spoke of Jon's parentage. Second, Ned was the most honourable man of them all, it's pretty unlikely he'd go off to war, newly married, and come back with a bastard son. Third, there's Ned's flashback to the Tower of Joy, where Lyanna is lying in a bed of blood and saying "promise me, Ned". We don't know what Ned promised; in my opinion, I think it may well be that Lyanna was left with Rhaegar's son (having fallen in love with Rhaegar; either like Dany did with Drogo, or she was always in on it and went off with Rhaegar willingly), and in her dying moments, pushed her son on Ned to raise as his own bastard. I find it more likely that Ned would agree to take Jon as his own at his sister's dying wish and the cost of his apparent honour than him legitimately fathering a bastard.
That's just me though. I can't really see a likely alternative as to who Jon's parents are, unless Martin throws a complete curveball and says "nah, he was actually Ned's bastard", which I also find unlikely. Realistically, what else is there? Jon clearly is a Stark; he's got the minor warg powers (like Bran but far less prevalent), he's got the Stark look (in the books certainly), etc etc. The main event that pushes me away from thinking he's part-Targaryen is the first wight encounter, in Mormont's chambers. When the black brother is revived as a wight, and Jon throws a lantern at it and burns the tower down to kill it; for the entire rest of the books, Jon's chapters mention him flexing his fingers constantly to prevent his burned hand from getting raw and broken. Dany (and Aegon the conqueror, I believe) however, had that immunity to fire; Dany likes her baths scalding hot, braved the flames to birth her dragons, just took it as Drogon burned Pyat Pree with Dany beside him, etc. However, Viserys and Aerys certainly did NOT have that immunity, and I don't know if it's certain that Rhaegar did. So it's certainly still a possibility, and the more you look at Jon's burned hand, the more you think psychologically, in Martin's mind, it may well be a way to put people off thinking he's Targaryen, when in fact he is.
But no-one really knows