Why does Kylo Ren wear a mask?

"Evidence-based" reasons:

1. A nod to Darth Vader

JJ Abrams spoke to Entertainment Weekly about the mask:

“The movie explains the origins of the mask and where it’s from, but the design was meant to be a nod to the Vader mask,” Abrams tells EW. “[Ren] is well aware of what’s come before, and that’s very much a part of the story of the film.”

So the first reason he appears to wear the mask is a nod to Darth Vader. This also follows an interview Abrams gave to IGN, where he said:

“Kylo Ren idolizes Darth Vader, not Anakin Skywalker. He idolizes what Vader represents and what Vader was trying to do. And the idea that Vader didn’t succeed, if you look at it from Ren’s point of view, he was seduced by the enemy and failed because of that seduction. So the idea is that Ren wants to complete the thing that Vader started.”

2. Avoid the conflict of his own emotions

The second reason does appear to be avoid his "human" side - to avoid the conflict of his own emotions. In the IGN interview above, Abrams also remarks:

“...And the story for him is one of conflict, not just internal conflict but external conflict. And it’s what makes him a rather interesting villain.”

Wearing the mask warps his voice and hides his face and whilst this primarily is a nod to Vader, it definitely makes him appear less human.

3. To be memorable

In an interview with Time Magazine, Michael Kaplan (the costume designer) remarked:

J.J. kept saying he’ll know when he sees it and one day we were having a discussion and he was talking about wanting it to be something that a child would remember, you know, that would be indelible in a child’s mind, and one of my concept artists came up with that image. I don’t know where he got it but he heard something that a child would like, and I don’t know if it was the kind of spaghetti type lines on it or what, but the next time J.J. came by that was what we presented to him and he loved it.

Now, this is very much an "out of universe" explanation, but it is evidence based. Abrams clearly wanted something memorable, scary and unique.

4. Conceal his identity

This is similar to Reasons 2 and 3 above, but I'm calling it out directly as this is explicitly stated in The Force Awakens Visual Dictionary. From Page 24¹:

Patterned after the battle gear of the Knights of Ren, Kylo Ren's helmet conceals his identity and adds to his imposing demeanor. Servomotors drive articulated arms that separate the face mask from the helmet, letting Kylo remove the black form to state down his opponents with [sic] incontained malice.

This is further contained by other sections of the Dictionary:

...his birth name is never spoken by decree of the Supreme Leader.

5. Military aspect of his character

Snoke tells Ren in the film:

"Even you, Master of the Knights of Ren, have never faced a test such as this"

We don't yet know what the Knights of Ren really are, but we do see the following image in the film²:

All of the people in this photograph are wearing masks similar to Ren's, so it's possible they are all the Knights of Ren.

As with every other militaristic group we see in the film series (from Jedi, to Sith, to Stormtroopers, to Clones, to Rebels) it's logical to conclude they have a uniform.

"Speculative" reasons:

Hopefully I've provided some reasonable evidence based reasons and given this I want to discuss just a few speculative reasons.

6. A nod to Darth Revan

Revan was a character from the Knights of the Old Republic video game series. This is his picture:

What is interesting about this possible link is the following spoiler:

We are introduced to Revan in the game as a Sith Lord, only to learn at the end that the protagonist we are playing as is Revan, and he in fact lost his memory. The Jedi Council chose to retrain him as a Jedi, rather than kill him, and in the game we can choose to be either good or bad - although the canonical ending is that we become good. This is obviously interesting as it could, repeat could, echo what will happen with Kylo Ren in the films to come.

7. To hide Adam Driver

The mask warped Driver's voice and hid his face. It made him quite scary, but also made him much more interesting as a character when his mask came off. He wasn't just a robotic or faceless enemy. This was a real, live person who got totally warped. He's not beyond redemption by any means. He's confused, he's scared, and he's dangerous. It makes him a very interesting antagonist.

Many people, myself included, wouldn't have known much about Driver, so seeing this completely "ordinary" person under the mask was actually quite startling.

To clarify, this doesn't mean to hide Driver because he is a poor character or actor, but because until the film all I heard was a scary voice in a mask. I never truly expected him to take off his mask in the scene with Rey. Seeing a truly ordinary man made the scene less fantasy and more real.

After all, look at the images below. The one on the left is far less scary, and yet it's the same purpose. He has done all these awful things. Putting a real face to a bunch of crimes, rather than just a helmet, is very powerful indeed.

8. Psychological warfare

To lift this point from a similar question at the Sci Fi Stack:

Psychological warfare. Vader was the death dealing wizard right hand man of the evil emperor for well over a generation. More than likely, his image is still enough to put a good portion of the population in fear. By taking up the mantle, so to speak, he is making a clear statement about the terror and power that he represents.

^{1: Thanks to @DVK at the Sci Fi Stack for highlighting this in his answer on that site.
2: Thanks to @Nathaniel at the Sci Fi Stack for highlighting this in his answer on that site.}

Kylo Ren wears a mask because he is infatuated with Darth Vader (see the scene with him and Darth Vader's mask), whose mask was very iconic, and as a symbol of power (see this SFF question for more information). Whether the mask has any special properties is not explicitly stated in the film, though the official dictionary says no.

• "Integrated vocabulator projects Ren's voice." (emphasis added)
• "Silver inlay radiates from the eyes as a symbol of power."
• "Kylo Ren's helmet conceals his identity and adds to his imposing demeanor." (emphasis added)

^{Science Fiction and Fantasy: Is Kylo Ren's mask instrumented?}

Kylo Ren wears a helmet because he is a space samurai. His helmet includes an integrated mask because he idolizes Darth Vader (another space samurai) and is commander of the stormtroopers (as Vader was), an elite space samurai corps (who all have masks integrated into their helmets). George Lucas was heavily influenced by the samurai films of Akira Kurosawa in making the original trilogy and has acknowledged this influence publically. Darth Vader's costume is a stylized version of samurai armor. J.J. Abrams is, of course, aware of this history and repeats these elements in his film to make it fit into the world Lucas created and feel authentic.