This particular crackpot theory has been fuelled by GRRM himself. Someone asked him, "Are Elia's children really dead?" at a signing, and GRRM's response was, "Well, certainly Rhaenyra died..." and didn't mention Aegon. Add in Rhaegar's belief that Aegon was the Song of Ice and Fire in Dany's vision in Qarth, and you have actually a perfectly respectable theory, and one that will almost certainly be addressed in ADWD.
Since Aegon was only one year old at the time, it would have been easy to substitute another young child for him and smuggle him to sympathisers in the Free Cities. And one of Rhaegar's best friends, Jon Connington, was in exile in the Free Cities at the time...
Thoughts on Aegon... and I'll see if I can crack some more pots...
I keep reading posts about how GRRM confirmed that Elia (Rhaegar's wife) and Rhaenys (Rhaegar's daughter) were murdered in the Lannister sack of KL, but that GRRM balked on the death of Aegon (Rhaegar's son).
So is Aegon alive? If so, where is he? Who is he?
Some time around the Battle of the Trident, Aerys II sent Rhaella (his wife), Viserys (his second son) and Danaerys (his daughter) to Dragonstone for safekeeping. When Rhaegar fell, terror must have gripped KL. Could Aegon have been switched out before Tywin sacked the city?
Iirc, Aerys II wanted Elia and her children in KL to ensure the continued loyalties of Dorne. I doubt he would have sent Aegon away. If that's true, then Aegon would have been secretly smuggled out. Obviously, Elia would have been in on this plot. But did she do it alone or did she have help? If she did it alone, she would have chosen a place that she knew would be safe, ie. Dorne. Her family would have protected Aegon. Or perhaps Elia had a friend, a female perhaps, who could pretend to be fleeing the fighting with a baby.
If Elia had help, who helped her? Varys, Rossart (the last Hand), and the Kingsguard would have been the closest and most intimate counselors to the royal family. Rossart was a Pyromancer, I doubt he had major connections for clandestine operations outside KL. Varys had his connections in the Free Cities... perhaps Varys knows where Aegon is. Here is an interesting thought... Jaime was the only Kingsguard in KL from the time Rhagar marched until Aerys II died. Perhaps Jaime knows something about this.
Another thought, Gregor murdered Aegon and Elia while Amory Lorch murdered Rhaenys. Amory had Rhaenys stabbed to death, like, twenty or thirty times... very guesome. Gregor, as we know, dashed Aegon's brains out against a wall. Given the superhuman strength of the Mountain, was Aegon even recognizable? If he'd been switched, Gregor inadvertantly made verification nigh impossible.
Also, when Tywin's troops entered the city, Jaime went hunting Rossart to stop him from blowing KL sky high. After killing the Hand, Jaime slew Aerys II. The next thing we know about Jaime is that he was sitting in the Iron Throne when Eddard Stark rode up. We don't know the time frame, but I can't imagine that Ned rode in while Tywin's troops were still trying to enter. There might be a few hours of Jaime's time that are unaccounted for... did he divert the Lannister's attention long enough for Varys to switch out Aegon?
So of the possible people who went through those times with potential knowledge, perhaps there are only Jaime and Varys still alive. Jaime felt pretty comfortable having Varys smuggle his brother out of KL on a moment's notice... it's almost like he'd seen Varys do it before.
Jaime is still in Westeros. Howland Reed is another person with potentially important, earth-shaking information, though probably not about Aegon.
Varys has gone into exile. Others in exile include Tyrion, Jorah, Barristan (who also served in Aerys II's kingsguard), Jon Connington (if he's still alive), Lynesse Mormont (Jorah's wife), Arya, Dany, and Ashara Dayne (according to one crack pot theory she fled and became Quaithe the sorceress). Dany and Arya were not even born when KL fell to the Lannisters. Tyrion was a small child. Jorah and Lynesse were on Bear Island, far from the royal family's machinations. Jon Connington was already in exile, but if he was one of Rhaegar's best friends as Wert says, then he may have been a contact for Elia or her conspirators. Barristan was with Rhaegar at the Trident... he was wounded and out of commission for a while. I would assume the Ashara was back home at the Dayne family castle.
My conclusion is that if you want to find Aegon, then look to Jaime, Varys (and by association, Illyrio), and Jon Connington (if he's alive).