I read a theory that Rey is a Kenobi and possibly a Skywalker/Kenobi making her super Force powerful. One tidbit it brought up is that the franchise is always very careful to get dialects and accents correct. The fact that Rey has an English accent like Kenobi could be a clue.
John Boyega (Finn) is English and Abrams had him use an American accent for Finn while Daisy Ridley, also English, got to keep her accent. We won't know until at least May 2017 but it is an interesting theory. The fact that Luke's light saber triggered visions for her is pretty telling that she is Skywalker - either by Luke or Leia.
I find it hard to believe that she's a Kenobi. Obi-wan was probably 60-ish* when he was killed and adhered pretty close to the Jedi Dogma, so it is unlikely that he had a child. Plus, since he was 40 at death, that would make any child he did have pretty close to Luke and Leia's age. At closest, she's a granddaughter (unlikely), but if she is a Kenobi, she would probably be a niece.
What we don't know is if the Council had some kind of reproduction program or something. Either a eugenics program where they select two compatible Jedi to breed better Jedi, or they just take biological samples of each Jedi to work with in the lab (a la Boba).
I still think the Skywalker (either Luke or Leia) connetion is the most likely option.
*Figuring he's 25 when they discover Anakin, 40 when he becomes Vader, and another 18 years for Luke to grow up.
Jedi were not allowed to marry by order of the Jedi Order, however, since it was disbanded after the clone wars. So this is why Luke ended up marrying Mara Jade in legends. Now, I will assume that since the Jedi Order disbanding is in canon, that Abrams could roll with the idea that since Luke was "the last jedi" as far as anyone was concerned, he could do what he wanted since he more or less had to figure out what being a jedi was by himself.
Friend of mind has a theory that Kylo is a pain focused force user like Darth Sion or Darth Nihilus. Could be very cool if they go that route. Also because old republic was awesome. Stupid Darth Bane and stupid rule of two.
Here's a link to an article that has some background with stuff that the movie didn't spell out for backstory - like i kept telling people it was NOT Coruscant that they blew up...but NNNOOOOO don't listen to me.... LINK
Yea and apparently the part of the movie where it is blatantly spelled out was cut. The hot girl that they show in the scene where the people are on a balcony looking up at the incoming death had a slightly bigger part but it was cut.