Rey is able to resist Kylo Ren, a practitioner of The Dark Side; she's able to wield a lightsaber; able to Force Pull the lightsaber; able to fly and fix the Millennium Falcon; able to defender herself; has Force visions, and the list goes on and on.
It might be fair to say that Rey might be the most powerful Force wielder ever?
With that said, let's take a look at some popular theories as to the identity of Rey.
1. Han and Leia's daughter: While it was said in the movie that Rey looked up to Han as a father figure, it's doubtful Rey is actually the daughter of Han Solo and Princess Leia, as it's probably a safe bet both Han and Leia would realize Rey to be their "long lost" daughter (if they had one). Plus, that would make Han and Leia even worse parents than originally thought (Kylo Ren, ahem).
2. Luke Skywalker's daughter: Just about the entire movie seems to allude to the fact that Rey is Luke's daughter. Rey is on the Light Side of The Force, she battles the bad guy, she finds Luke's lightsaber (or the lightsaber finds her), she goes on a quest to find Luke, Maz tells her she has seen her eyes before, and of course, she finds Luke at the end of the movie. However, this theory could just be too obvious, with perhaps Abrams and Disney trying to steer us in the wrong direction.
3. Relative Of Obi-Wan (via Yahoo): Could Rey be related somehow to Obi-Wan Kenobi? It's possible, and there is even one fan-theory suggesting Rey may be the daughter of Luke Skywalker and Obi-Wan Kenobi's own daughter; however, we haven't heard anything about Obi-Wan having a daughter in any of the movies, have we?
4. Reborn Anakin/Darth Vader (via Inquisitor): Another fan-theory suggests Rey may actually be a reincarnated Anakin Skywalker. I'm not sure how much merit this holds as we've seen Anakin's Force Ghost; however, it's alway possible that Snoke may have a Dark Side power of bringing back the dead (somehow). It could also be argued that Rey has more in common with Anakin than anyone else, which leads us to...
5. Conceived by The Force similar to Anakin (no father): I thought of this one. As Rey is so powerful, does she have a similar origin to Anakin's? As we saw in Phantom Menace, it was said Anakin had no father and was conceived by The Force. It's possible the "force has awakened" and created Rey. We could even go further and suggest that Rey may go a similar path to Anakin and turn to the Dark Side herself.
The last two theories suggest that Rey was a Jedi serving under Luke Skywalker when the tradgedy occurred that sent Luke into hiding -- with the Padawan that killed all the others. This also helps explain why Rey can use The Force (as she already had prior training).
6. Evil Jedi - mind wiped: Rey is the evil Jedi/padawan who killed all the others, but Luke mind-wiped her and planted false memories as he didn't want to kill her. This could also explain why Rey had such strong feelings to stay on Jakku -- because Luke implanted that into her because he never wanted her to leave.
7. Luke's apprentice who survived (via reddit): It's possible Rey survived the slaughter, and Luke hid her on Jakku so as not to get killed. In the process, he mind-wiped her and planted false memories to either protect her, or as he felt like he failed, to not have any more Jedi (and never wanted her to leave).