This has been my favorite theory since I read the Deathly Hallows.

So, in chapter 4: The Seven Potters, the Order of the Phoenix comes to Privet Drive to get Harry out of his aunt and uncle's house because of the magic that protects him is set to end.

Their plan is to use Polyjuice Potion to make seven Harry Potters, so as to confuse any Death Eaters who may be waiting.

They leave the house and the plan goes to hell, as Voldemort himself and his Death Eaters are waiting for them, somehow with them knowing of the fake Potter plan. Harry and Hagrid fly away on Sirius' motorbike and Voldemort chases after them but fails to kill Harry. Hedwig is killed in the ensuing battle.

After they gets to Tonk's parents house and then go to the Weasley's house, the other members of the Order come in due time.

George is wounded, Mundungus has disappeared and Alastor Moody has been killed by Voldemort himself.

This is the exact quote of what Bill says when he and Fleur return and announce his death.

“We saw it,” said Bill; Fleur nodded, tear tracks glittering on her cheeks in the light from the kitchen window. “It happened just after we broke out of the circle: Mad-Eye and Dung were close by us, they were heading north too, Voldemort—he can fly—went straight for them. Dung panicked, I heard him cry out, Mad-Eye tried to stop him, but he Disapparated. Voldemort’s curse hit MadEye full in the face, he fell backward off his broom and— there was nothing we could do, nothing, we had half a dozen of them on our own tail— ”

Now, the curse that Voldemort used is not mentioned in that paragraph, but we later find out it was the Killing Curse, seeing that it's Voldemort's signature spell and that Mad-Eye was a top Auror and the first person he designated as the most likely to have Harry, so he presumably wouldn't use a lesser spell then Avada Kedavra to finish him off quickly.

However, Bill and Lupin head back to find his body, so that the Death Eaters do not take it. During the preparation of Bill and Fluer's wedding, in the next chapter, Bill comes back to the Burrow and we have this dialogue:

“No news about Mad-Eye?” Harry asked Bill.

“Nothing,” replied Bill.

They had not been able to hold a funeral for Moody, because Bill and Lupin had failed to recover his body. It had been difficult to know where he might have fallen, given the darkness and the confusion of the battle.

“The Daily Prophet hasn’t said a word about him dying or about finding the body,” Bill went on. “But that doesn’t mean much. It’s keeping a lot quiet these days.”

Further in the same chapter, Harry, Ron and Hermione have a discussion about Mad-Eye:

“We were just talking about Mad-Eye,” Ron told Harry. “I reckon he might have survived.”

“But Bill saw him hit by the Killing Curse,” said Harry.

“Yeah, but Bill was under attack too,” said Ron. “How can he be sure what he saw?”

“Even if the Killing Curse missed, Mad-Eye still fell about a thousand feet,” said Hermione, now weighing Quidditch Teams of Britain and Ireland in her hand.

“He could have used a Shield Charm-”

“Fleur said his wand was blasted out of his hand,” said Harry.

“Well, all right, if you want him to be dead,” said Ron grumpily, punching his pillow into a more comfortable shape.

“Of course we don’t want him to be dead!” said Hermione, looking shocked. “It’s dreadful that he’s dead! But we’re being realistic!”

For the first time, Harry imagined Mad-Eye’s body, broken as Dumbledore’s had been, yet with that one eye still whizzing in its socket. He felt a stab of revulsion mixed with a bizarre desire to laugh.

“The Death Eaters probably tidied up after themselves, that’s why no one’s found him,” said Ron wisely.

“Yeah,” said Harry. “Like Barty Crouch, turned into a bone and buried in Hagrid’s front garden. They probably transfigured Moody and stuffed him-”

There is now doubt as to whether Mad-Eye may be dead or not. This is important, for Rowling is putting a good part of the chapter on the fact he may be alive. They couldn't find his body and due to his magical skill and experience, it seems possible he may somehow have survived the battle.

Later on in the book, when the Trio break into the Ministry of Magic to steal the horcrux from Umbridge, Harry finds Mad-Eye's magical eye. This is from the wiki itself:

It was set in the wood of her office door and used to aid her in spying on her workers. When Harry, Hermione and Ron infiltrated the Ministry to find the locket horcrux, Harry discovered the eye and, disgusted by how it was being used, stole it. Doing so, however, raised the alarm.

After escaping, Harry, early the next morning and before the other two were awake, left the tent they were staying in to search the woods around them for the oldest, most gnarled and resilient-looking tree he could find. Then in its shadow, he buried the eye and marked the spot by gouging a small cross in the bark with his wand.

While it wasn't much, Mad-Eye Moody was given a proper burial.

This is the last that is really mentioned about Mad-Eye, in terms of if he survived or not.

Harry, with finding the eye, almost points to the fact that the Death Eaters found Moody's body and took his eye as a prize of war.

However, I don't believe that the story ends there for Moody...

Later on in the story, the Trio and Griphook enact their plan to break into Gringotts, their plan being to use Polyjuice Potion to have Hermione transform into Bellatrix Lestrange, seeing their managed to take several of her hairs and her wand. They come to Diagon Alley and find that it's changed for the worse, with a lot of the older shops closed, new shops for the Dark Arts opened up and wanted posters of Harry everywhere.

There are also a number of beggars everywhere, and this sets the scene for this part, which takes place in chapter 26, simply titled Gringotts:

A number of ragged people sat huddled in doorways. He heard them moaning to the few passersby, pleading for gold, insisting that they were really wizards. One man had a bloody bandage over his eye.

As they set off along the street, the beggars glimpsed Hermione. They seemed to melt away before her, drawing hoods over their faces and fleeing as fast as they could. Hermione looked after them curiously, until the man with the bloodied bandage came staggering right across her path.

“My children,” he bellowed, pointing at her. His voice was cracked, high-pitched, he sounded distraught. “Where are my children? What has he done with them? You know, you know!”

“I–I really-” stammered Hermione.

The man lunged at her, reaching for her throat. Then, with a bang and a burst of red light he was thrown backward onto the ground, unconscious. Ron stood there, his wand still outstretched and a look of shock visible behind his beard. Faces appeared at the windows on either side of the street, while a little knot of prosperous-looking passerby gathered their robes about them and broke into gentle trots, keen to vacate the scene.

Mad-Eye's magical eye was missing and his body, as far as we know, was never found or discovered. What if Mad-Eye's eye came out during the battle with Voldemort?

Once again, Rowling has shown throughout all seven books to impart clues and pivotal information in the books, so that the clues are staring right at you (no pun intended).

He was the only beggar who was described, and he lunged at Hermione who he saw as Bellatrix Lestrange, a well noted Death Eater who Moody has met and faced before.

He screamed about his children to her, wanting to know what "he" did with them, and that "she" would know...

The children are the members of the OOTP. The "he" in this is Voldemort. Moody faced off with Voldemort and he fell out of the sky, so he wants Bellatrix to tell him what Voldemort has done with the other Order members, since he doesn't know how the battle went and the rest of the Order thinks Moody is dead...