We can all agree that titans are creepy as hell, but other than that, what exactly are they? The manga has not yet revealed what they are or where they come from, but I've had a theory for awhile now. The manga is still ongoing, so I don't have all the answers, but I will not spoil anything here, for those who have only watched the anime. I got the idea from Commander Pixis' lieutenant, back in episode 11 or so, who said something to the effect of, "if you could control a titan, what a great weapon it would make." Incidentally, that's just what I think titans are: biological weapons. (Everything henceforward is pure speculation, mind you.) I think that over 100 years before the story opens, mankind developed a vaccine to harness individuals' primal desires and strengths to manifest "titans". The world was at war, and they were the ultimate weapon - practically indestructible, lightweight, powerful. The perfect killing machines.
As we know from Hanji's research, the titans' bodies should be extremely heavy, to the point that they shouldn't theoretically be able to move on two legs with all that mass, but they're instead impossibly light; they defy the laws of physics and nature. We know that they have no need of eating to sustain themselves. They ignore other living creatures, but gorge on humans until their bellies are full. Then they vomit up a sticky ball of undigested body parts, as if to add insult to injury: "I don't need to eat you to live or anything, but I'm going to anyway, just because I can. Nyah-nyah-na-nyah-nyah."
Here's the scary part of my theory: All the titans outside the walls were once, themselves, human.
I think, at some point in the distant past, everyone was administered the vaccine. In future generations, it eventually became part of our DNA. That's right, I think that everyone has the dormant ability to transform into a titan. So why don't they, and why does Eren? Well, it obviously has something to do with the shot his old man gave him before he disappeared (by the way, I think this caused Eren's first titan transformation, when he then lost control and either ate or killed his dad).
But then, you ask, if all those titans are housing humans, why do they kill people indiscriminately? Because they've lost their humanity to their basest instincts, I reply. They're like zombies. Once base instinct takes over, nothing remains except the need to feed. The fact that they're just meaty weapons and have no actual need for sustenance doesn't occur to them. We can see this beginning to happen to Eren in his titan form when he comes face-to-face with the female titan and pins her down in the woods. We saw it earlier, too, when he lost control and attacked Mikasa, but the forest is a more concrete example because he didn't try to eat Mikasa. While waiting for his hands to regenerate, his inner monologue tells the female titan, "I'll rip you apart, I'll devour you bit by bit." The key word here is "devour". In Japanese, it's the same word the soldiers use when a titan "devours" a human. Granted, Eren is a little on the extreme side, but he becomes more and more animalistic the more he allows his titan form free reign of his instincts. if he were to continue to let himself go, he would eventually end up just like all those other mindless titans, nothing more than an eating machine. This is what happened to the human weapons who ended up pushing humanity to the brink of extinction: they lost themselves to their basest instincts, condemned to wander the world as titans and consume their own kind, forever. (Why don't they die, though, trapped in a titan's body with no means to sustain their actual, human existence? That, I'm not sure of yet. The only thing I can think would be that it induces some sort of suspended animation state.)
Or, that's what I think anyway. It's tragic. But this show/manga is categorized as "tragedy", remember.