It is becoming of very popular opinion that the mysterious character Snoke introduced in Episode VII is actually a character briefly discussed in Episode III, Darth Plagueis. We know very little about Snoke from the movie as the only time we saw him was when he spoke with Hux and Kylo Ren as a holographic image. However, by using context clues from Episode III and some facts from the book Darth Plageius written by James Luceno there are many reasons to believe Snoke and Plagueis are the same character.
In Episode III, Palpatine tells Anakin the story of this Sith Lord named Plagueis and how he could save people from death. Palpatine also tells Anakin that his apprentice (Palpatine) killed him and learned all of his powers. We can tell later in the movie that Palpatine truly didn't learn how do cheat death as he tells Anakin that together they will have to work to figuring it out. Palpatine doesn't tell us much else about Plagueis.
Warning: this next section will contain spoilers from the book.
Now, in the book written by James Luceno the entire background story of Darth Plagueis is given. We know he researched many types of species that have different abilities in an attempt to discover immortality. One of the powers that Plagueis possesses is the ability to create Force Illusions. When Plagueis first takes Palpatine under his wing he uses one of these Force Illusions on Palpatine. Palpatine was under the impression that Plagueis was right in front of him when in reality he was speaking to nothing. If Plagueis was actually so powerful he could have done one of two things.
The first concept could be Plagueis used a Force Illusion tactic on Palpatine and never truly died. Although this is a bit more far fetched it wouldn't be too drastic of a concept to believe. We know Plagueis was a very powerful Sith and could have used these illusions to spare his life. The other possibility could be that Palpatine actually did kill Plagueis, for a moment. Plageueis is of the Muun species which is known to have three hearts. There is a possibility that Plagueis could have been dead for a moment but the midi-chlorians in him could have actually brought him back to life. Being scared from his attemptive murder, Plagueis then went into hiding until he could face anyone again.
The concept of Plagueis going into hiding could be very feasible. Knowing that Palpatine was becoming very powerful in the Force, Plagueis wouldn't stand much of a chance in the state he was in after his attemptive murder. Thus Plagueis went into hiding allowing the Jedi and Palptine to duel taking out anyone who could come in the way of his ultimate conquest of becoming immortal. Being of great wealth and already having an established identity of Hego Demask, it wouldn't be too far to think Plagueis could come up with another identity of Supreme Leader Snoke. Snoke fits the description of a Muun and there are many images leaked showing the similarities between Plagueis and Snoke.
Just For Fun:
Another theory I have that doesn't have as much evidence to back it up is that Plagueis actually created Anakin Skywalker. In Episode I Shmi Skywalker tells Qui-Gon that Anakin was conceived without a father. This is obviously something strange that was never really addressed in any of the movies.
In the book we do learn that Plagueis invested in the pod racing track on Tatooine and had a presence on the planet due to this. Plagueis could have sensed his time was limited so creating another strong being that the Jedi would find would suit him well. By creating Anakin he could have set up the whole situation in which he would be able to take out the Jedi and also take out Palpatine eventually.
We know Plagueis wasn't too concerned about Palpatine as a person but more so just wanted his assistance and political powers to while out the Jedi. By creating Anakin, Plagueis would take out his advisary eventually. In addition he would have some sort of connection to the offspring of Anakin in the future. This could be another reason why Kylo Ren is loyal to Snoke. Although this is a concept with very little support I do think it is a possibility and was worth noting.