Han and Leia's. I know it seems a little crazy (or it might be being floated elsewheres regularly), but the idea fits so well.

Yes, it would seem that Han/Leia should recognize her, and they actually do know who she is (at least Leia -- see end hug), but they can't say anything to her on this. They have hid her away from her older brother who is twisted by the force and who would seek her out to kill her. This plays with our sense of how much older her might be -- perhaps 7-8 years older and Leia became pregnant after he left. This makes so much sense of the arc of the movies -- allowing us the masterful rewatch value down the road once it is revealed (the fight in the woods, Han trying to hire his daughter to travel with him, Rey watching her father killed, etc.). We see a different archetypal struggle play out, that of brother vs sister / the masculine vs the feminine side of the same coin.

It also makes sense on the level of postmodern movie reveals: we all expect her to be Luke's daughter and it is the perfect red herring they can string us along with. Star Wars has never played with off-screen set ups of the secrets (like the way a crime movie might go back a show what happens just before or after a scene to show that the person we didn't think knew something, actually does). This is in part, because it's a little unsatisfying when the twist rests on something like this, but I think (and I think JJ thinks people will think) that this is a worthwhile trade off in order to provide a twist that not many people will see coming -- hard to do in this day and age. Unfortunately I might be ruining his plan by airing this theory all ready.

The only other weak spot in the theory is that we might expect Kylo Ren (notice how related their names are) would have felt Rey's relation during their battle or something else, but this might be explained in a couple different ways -- not least among them that Kylo is just an amateur with the force yet.