Seven Extremely Geeky Questions Raised by Star Wars: The Force Awakens
Was Rey trained earlier?
For someone who didn't know she was a potential Jedi, or even that she was Force-sensitive (or that the Jedi and the Force actually existed), Rey suuuure gets the hang of things quickly. She's able, in a small span of time, to fight off Kylo Ren's psychic attack, successfully use a Jedi mind trick, Force pull, and defeat an enemy trained in both light and dark side tactics in a one-on-one lightsaber duel.
So that all begs the question: if she was left on Jakku as a child, was she trained, at least for a year or two, before-hand? And if so, why didn't she remember it? It's very possible her memories were locked, only to resurface when Kylo Ren started digging around and she touched her (presumed) father's lightsaber. It'll be interesting to see, when her training presumably starts in earnest in Episode VIII, just how much she truly remembers.

Who (and what) the heck is Snoke?
One of the bigger mysteries leading up to the movie was just who Supreme Leader Snoke was. Unfortunately, that mystery didn't get anywhere close to solved.
We only saw Snoke as about a 100 foot tall hologram. He's old, clearly, and scarred, as actor Andy Serkis had teased. He seems to know the dark side of the Force, but we don't actually know if he can use it. We thus also don't know if he's actually Sith, or just someone trying to bring about their rise.
In the end, Snoke here was nearly as enigmatic as The Emperor was after the first two movies, despite quite a bit more screentime. Can't wait to find out more about who he is and what his plans are.

Where are the current Force-sensitive younglings?
When Rey saw, through the Force, that Kylo and the Knights of Ren slaughtered the younglings that had been training with Luke, there were at least ten-twenty bodies on the ground. But that was a generation earlier than the events in the film.
So where are all the Force-sensitive kids now? As we've seen, they never stop being born. It was a major topic in both Star Wars: The Clone Wars and Star Wars Rebels, in the latter they've been taken by the Empire to be trained as Inquisitors. With a generation gone, there should be a whole new crop of kids in the waiting, strong in the Force.
So where are they, and will that be addressed in the future? Is Snoke actively recruiting them for his own Knights of Ren?

Who is Rey’s mother?
If we're correct, and Rey's the daughter of Luke Skywalker, which she seems to be thanks to her connection to the lightsaber and her memories of where Luke could be found, then it does bring up another question: who is her mother?
Jedi, traditionally, aren't supposed to marry - the attachment of a family is too big a risk to turn them to the dark side. Of course, in the defunct Legends stories, there were plenty examples of this being flaunted, but most of those examples led the Jedi down a dark path, seemingly confirming the rule should be kept. Anakin Skywalker is the only Jedi in canon to marry and, well, that didn't go so well.
Also in the Legends universe, however, Luke married another Force-sensitive named Mara Jade, and had a child (a boy, though). Luke never turned to the Dark Side from this coupling.
So, if Rey is Luke's daughter, there should be a mother, either a wife or someone who was very close to Luke for a time, somewhere out there. It's possible she was killed, perhaps even by Kylo Ren and his ilk, but even if she's already dead, she's extremely important and interesting.

What, exactly, are the Knights of Ren?
The Knights of Ren. We've mentioned them a few times, now, but we don't really know who or what they are. The Sith shared power amongst only two people for generations, though they did allow for other dark side Force users like assassins and Inquisitors. While the Knights are mentioned, they're only seen in the flashback Force vision, which begs the question: where are they now?
We also don't know if they're all Force-sensitive, if they're still around, if they're in other parts of the galaxy, if they have any direct connections to Kylo and Snoke and the First Order. It's basically its own set of top five questions here. Hopefully, we'll learn more about this group in the next two movies (or at least in some novels or comic books).

Why did Luke stay away for so long?
We can debate, easily, why Luke left in the first place. He was told to "Pass on what you have learned" by Yoda, and started to. But one bad apple rises up, and he disappears?
Some people think Luke left out of guilt, thinking he'd made the galaxy worse off and couldn't do anything to change that. Others think he left to find a solution, hence going back to the first Jedi temple. But even if that was the case, why stay gone for so long? He had to be gone for at least a decade and a half, given Rey's age, and if he hadn't found the solution in that time, you'd think he'd come back to try something new, especially as the First Order rose in power.
Luke's journey is obviously far from over, and with the teaser at the end of the movie, we can bet we'll learn more about it in the next film.

Why didn’t Leia train as a Jedi?
Now this is a huge question. Yoda explicitly told Luke to pass on what he'd learned (as mentioned in the previous entry), and that there was another Skywalker. Luke, upon telling Leia about her origin, said to her, "You're wrong, Leia. You have that power too. In time, you'll learn to use it as I have."
So... why didn't she? Leia doesn't do anything in Star Wars: The Force Awakens to indicate she ever had Jedi training. She's clearly still naturally strong in the Force - she feels it when Han dies several light-years away, but she sure doesn't have a lightsaber or go into any kinds of Force trances or anything of the sort.
It's baffling, then, why she didn't. Was it merely her becoming a mother, she wanted to dedicate her time to that? Did she hesitate both becoming a leader in the Republic and Resistance while also dedicating time to gain mastery over the Force? It's hard to tell, but hopefully in the future films we'll get to see Leia Force push a stormtrooper or wield a lightsaber at least once.
