Force Awakens Spoilers Ahead!
Her Force abilities seem to indicate that she's the daughter of one of the Skywalker twins. But is she the daughter of Luke, or Leia?
Brown eyes and brown hair. That seems to point to Leia, but it could also point to Padme, Luke and Leia's mother, or even Shmi Skywalker, Anakin's mother. So let's let that rest for a moment.
How could Luke have a daughter? The only Jedi who dared to get into a relationship was Anakin... and that pretty much was what turned him to the Dark Side. Unless Luke somehow got secretly married without someone knowing about it, like Leia for instance (who is Force-sensitive), he's most likely still how George Lucas wanted him to be: Single.
And what is with Rey saying the same phrases as Han Solo, at the same time?
Unless she was around them before, or in the Millennium Falcon before, how would she know how to get it to work, and fix it when it starts failing?
Also, when she wakes up across from Kylo Ren (a.k.a. Ben Solo) in the First Order base, and he takes off the mask... she has an expression of many emotions, when she sees him unmasked. She's seen his face before, but can't place it. Could she have been one of the younglings Luke was training when Ben Solo turned to the Dark Side and attempted to kill all the younglings? How did she escape? And how did she end up on Jakku, in the same area of the planet as the missing map piece held by the elder, until Poe Dameron got it, gave it to BB-8, and told him to get away?
How does Rey understand BB-8 and later Chewie? Does she just listen to all the people, creatures, and droids who come through there (a reference to Anakin as a child), or is there something more to how or why she understands them?
How does Maz Kanata know her eyes? And where did Maz get Luke's old blue lightsaber, supposedly lost when it fell to Bespin from Cloud City in Empire Strikes Back? And Rey's visions when she touches the lightsaber... what do they all mean?
We're all seriously speculating who Rey is... but one thing's for sure:
We'll all have to wait till Star Wars Episode VIII comes out in 2017 to find out.