OBVIOUS SPOILER WARNING
I have seen the entirety of the show and one chapter of the manga right were the show left off. If you have not at least seen the show to completion, MAJOR spoiler warnings mixed in with my assumptions.

Theory :The Titans
Going by everything I've seen, I believe they're infants: creatures recently given life. It's so obvious in their mannerisms and awkwardness, some can't even walk right. Like a baby, they only care about fulfilling their most basic and urgent need, however that is not hunger. Titan's don't need sustenance, and they only attack people, not animals. This isn't hunger causing them to eat people, but it's still a need they mindlessly follow. The characters in the show are aware of this, but they believe it is because the titans want to annihilate humanity. Obviously that's not the case because these things don't even really think, how could they possible want to annihilate anything?
Given the obvious complexity and thought that went into this world, I believe the show gave a lot more hints then most people are aware. When Eren and Annie turn into Titans, their human bodies are in the back of the neck, the same weak spot for regular titans. The difference being that on regular titans there is nothing there but flesh. I think one of the characters even casually mentions how odd that is. In stories so draped in mystery, it's always important to catch the small things like that. Because this is also the only vulnerable part of the regular titans and vital for them to exist, I believe this is essentially their "control center". I mean that literally, because I think the titans are more-or-less living machines: living machines searching for their missing part, and that is why they only eat humans. Humans are the missing part, and the titans mindlessly consume them because they are oblivious how to genuinely integrate with them. They eat and eat and eat not realizing why that void hasn't been filled, even though they're putting the right part inside themselves.

This would also explain why the regular titans still attack titans like Eren and Annie, because they have the part that's being sought after. I also believe the titans are matter transmogrified; basically the process Eren goes through every time he transforms? Yeah, that, only with anything. Again, as I mentioned above, the titans are missing their human component, that's why they're after only humans. I believe whatever that is that happens to Eren could basically happen to anything, even possibly inanimate objects or plants. I am sure to mention plants especially because they go out of their way to specifically mention that some titans go dormant at night and need sunlight to be active, but only SOME. Again, I have to assume they are leaving clues to the mystery here, just like they left clues for certain other things I'll get to. It would certainly explain the way the titans behave. They act very much how I'd imagine something inanimate that was just given life.

Theory: The characters
Yes, I know who the colossal and armored titan are. I was one of the unfortunate people caught in the comment spam on youtube and all other social media places. You know, the whole "Snape killed Dumbledore" shtick. It's fine though, looking at the clues it was pretty obvious, especially considering who they consorted with (and that's all I'm going to say about that). However I don't believe that is the biggest bombshell.

My theory about the characters is this all isn't about the origins of a hero, but a villain. Eren is the villain of this story. It's perfect, he starts out as a regular kid, he's sympathetic, he has friends who care about him... Adult Eren is a monster, he's crazy, everyone sees it in his eyes, and at the end of the first season he really let all that show, killing innocent people left and right just to stop one titan. He even says "I'll destroy the world". I don't believe he was just spouting random nonsense in his rage, everything in this story seems very deliberate. Also the Armor titan, Colossal titan and Annie are all the "goodguys". They're good people trapped in a horrible situation who have to do something terrible, or they created a horrible atrocity in order to somehow avoid an even greater one. I can't say exactly what the specifics of that could be, but I have ideas that I'll soon touch up on. In any case it would be pretty amazing if this series ended with people rooting for Eren to be stopped for everyone else's sake, especially considering how this story began.

Theory: The world
I found this entire story suspicious from the very start. It's one thing to tell people it's dangerous outside, it's another to make knowledge of the outside world outright forbidden. I don't believe for a second the world really is overrun with titans, there is too much secrecy and too much "stop asking questions and just believe what we tell you" attitude around that whole show. So if the world really isn't overrun, why is everyone trapped in these walls? It's likely connected to why the colossal and armored titan originally attacked. They don't want people in this location for some reason, and considering they're willing to kill hundreds of thousands of innocents, it must be a damn good reason. It is entirely likely the fate of this world hangs in the balance. Even more creepy, I don't believe the walls are there to keep titans out, but to keep people in. I have a sneaking suspicion who or what is creating the titans is only doing it outside of the walls and doing so in order to keep the people inside, because they need them and they need them there. This is obviously going to have a very bad outcome, which would likely start to justify what colossal titan did. So yeah, the titans aren't an invading force, they're jailers, and Eren was right in what he said at the very beginning: their home was literally a pen. I honestly wouldn't even be surprised if humanity did still exist outside the walls and the world really was a populated place.

For those who have read all the manga, PLEASE do no tell me if I am right or wrong, assuming the manga has even explained anything yet. I purposely avoided catching up to the manga just so I could enjoy the WTF factor of season 2 like I enjoyed season 1. I don't even care if I am wrong, I just like to try and test my powers of observation. XD