I hope Luke is Rey´s father. I know many might object that it would be too obvious. And indeed, wievers sure recieved a lot of hints to think so.
They kind of look alike, or at least as much as one might wish, concidering their family traits. Anakin was blond with bright eyes, whereas Amidala had brown hair and brown eyes; Leia´s hair and eyes are also brown, while Luke is fair - despite the fact they are twins. Rey has brown hair and her eyes are probably somwhere between green and grey. But the shape of their faces might be considered familiar.
She certainly shows more likeness along the way. We can see she is genious technician, solving problems instantly or able "to fix anything". Doesn´t that sound like something everyone of us already heard somewhere before? And there is more: she sure seems like a natural pilot (I do not even mention that fighter helmet scene, where she resembles kid Anakin A LOT). As far as we know, she has never operated anything bigger than a hovercraft yet she manages to pilot the Falcon like she has been doing it her whole life! We can definitely add to the evidence the fact that Luke´s lightsaber was calling her - it looks rather significant along with the vision she recieved when touching it. Her superior ability to control the Force without any previous training merely lies on top of the pile. We may as well pass the pararells of pulling lightsabers out of snow, of being probalby guarded by some grandpa and growing up on desert planets (desert planets and relative poverty - so far Skywalker main protagonists share these). Also, Chewie likes her instantly and there are some hints suggesting Kyle Ren expected her appearance on the seen sooner or later. She is getting along with the old gang pretty well, R2D2 woke up after she appeared etc.
Now, I understand there are some problems concerning the timing. I am certainly no expert but I don´t see any. She must be younger than Ben (Ren), in any case - but why not? Noone says that Luke just hid under a rock on some old deserted Jedi temple immediately after he vanished. There must have been plenty of time for him after giving up training new generation to fall in love or at least obtain himself a kid. It would also explain why nor Han neither Leia made an obvious connection (no that we know of) after Luke´s sword reappeared on the seen (at least Solo knew about this particular Jedi weapon) - which they probably would, if they knew of Luke having any children. More questions, on the other hand, arise from Rey not remembering who her parents are - even though she was already five, when abandoned.
And least but not last - and everyone seems to forget about this side of the story: we have been, from the very beginning, following the destinies of Skywalker family. And everything started with a miracle child who should, in some way, bring balance to the Force, or save the galaxy... We have always been told to expect something like that, a final conclusion to this basic plot - but are we certain it happened? There were hints, especially in first three episodes, but nothing certain. Was the "saviour" really Anakin? How could he, when he fallen to the dark side. Or was it because he turned to the light again? I highly doubt that. There have been many Jedis with some inclinations or encounters with the dark side (in Clone Wars, we met several or at least heard about them - so it is no big deal). Then was it because he fathered two children who might accomplish the deed? But nothing like that was ever offered to us as explanation - that Luke would be the one from that old prophecy. On the other hand: we learn that he failed raising new generation and there is still no balance at all. So wouldn´t it make sensce to build up the story to its final conclusion, connecting all those dots and threads and at last explain the whole prophecy thing?
At this point, creators of the new series can choose from many options how to solve Rey´s connection to the story. If she is not Luke´s child, I believe they certainly made a lot of effort to have us believing so. As I said, I would prefer if she was indeed Rey Skywalker. I would love her to return to the old Jedi order - before episode one, to return to the roots. Or she might turn everything upside down, bring balance to the Force by destroying the concept of Light and Dark. These are all uneducated guesses. But might be worth at least some consideration. I do hope you all enjoyed the new film and are thrilled to no. VIII.