THIS POST CONTAINS NO SPOILERS only speculation and guesses!
Now that Harry Potter and the Deathly Hallows has been leaked online, I decided I'd put my forecast for the book out there before I hear details through an accidental glimpse at a web site or the slip of the tongue of some overzealous fan.
First let me say that I've read a lot of speculation about the Harry Potter Books and some theories I really like and some are really silly (Snape is Nagini). The theories that I like have really influenced my thoughts about Deathly Hallows and my forecasts for the book are pulled largely from other sites that have presented strong evidence pointing toward likely story elements. I will link to those pages that strongly influenced my thoughts.
I am a subscriber to the theory that books 1 and 2 are parallel books to 5 and 6, and that 3 will be a parallel to book 7, with book 4 being the fulcrum on which the series swings. The basic idea is that plot elements are repeated between the parallel books. The Red Hen lays out that theory along with examples here.
With that in mind, I think there are some Prisoner of Azkaban elements we can expect to see in Deathly Hallows:
Stan Shunpike will be released from Azkaban due to Harry's actions (Maybe Scrimgeour, facilitates this as an act of good faith toward Harry and his cause) and I think we'll take another ride on the Knight Bus.
Harry will face a dementor's kiss once again. Possibly to remove Voldemort's soul fragment from his scar.
Harry will leave the Dursley's after his birthday (possibly on the Knight Bus) after his final confrontation with Petunia and Vernon, and spend some time at the Leaky Cauldron.
We will see at least one more boggart.
Harry might use the Shrieking Shack as his base of operations in Hogsmeade. If not we will pay at least one visit to the shack.
Trelawney will make one more true prophecy.
Werewolves will be important, and Bill Weasley may have to deal with becoming one. (Another possible use of the Shrieking Shack?)
Buckbeak will have an important part to play at some point.
Time will be an issue, but a time-turner will not necessarily be involved.
Check out the Red Hen page for more speculation on Azkaban parallels.
Based on another pattern that Rowling has incorporated into the novels is the notion of introducing a magical concept and it becomes paramount two books later.
In book one we meet our first Animagus, and Azkaban was ALL about Animagi and the possibilities inherent. Book 2 showed us how a Pensieve worked via the Diary, then we see the Pensieve proper in Book 4 and Book 6 was full of Pensieve usage. This also makes me wonder if we didn't see a Horcrux in Book 4, but nobody has realized it, or theorized about what is is(that I know of). I personally don't have any ideas on this other than the relevant pattern. Book 3 showed us our first prophecy and Book 5's plot pretty much hinged on the quest to retrieve Harry's Prophecy.
Book 5 introduced us to Tonks the Metamorphmagus. This concept has yet to be fully explored and I think metamorphmagi will play a part similar to the animagi in Azkaban. Someone we know is either not what they appear and never has been, or someone we know is really someone else, hiding in plain sight (Regulus Black?)
Other Things I think we can expect to see:
Hogwarts will be open, but possibly with a limited student body, or maybe only part of the year. Harry will spend significant time at the school.
Luna Lovegood will be vindicated with one of her crazy Quibbler stories. Perhaps we'll confirmation of the existence of a Crumple-Horned Snorkack, possibly something else.
Harry gets a new Patronus, possibly a phoenix, possibly something unique to Harry as he becomes his own man.
Snape is revealed to have been working his own game, playing both sides against the middle(ala Machiavelli's Prince), but will still redeem himself in the end. The theory presented on the Hogwarts Professor page is almost too overwhelming to ignore. That site thinks the evidence points to Snape being all evil, but I think redemption is still possible and highly likely.
The final battle/confrontation will involve an underground cave, tunnel, chamber, maze or tomb as it has in every single book.
Deathly Hallows will have a body count. Among the dead will be the following in categories of Certain, Likely, and Possible.
Hagrid - All of Harry's father figures pay with their lives, Sirius, Dumbledore and finally Hagrid.
Wormtail/Peter Pettigrew - He'll pay his life debt, but will not survive.
Snape - Even if he's good, he is in such a precarious position that survival is unlikely.
Bellatrix Lestrange - Neville gets to avenge his parents.
Voldemort - He dies, he has to die to complete the story.
Draco - In a position similar to Snape, but with better chance of survival, as he hasn't actually killed anyone, but that could do him in on the Voldemort side of things.
Remus Lupin - I just don't get the feeling that any of the Marauders walk away from this story. He may get killed by his fellow werewolves.
Numerous Death Eaters and Order of the Phoenix - Some of the named members of these groups will buy the farm adding gravity to the war. MacNair, Crabbe, Goyle, Shacklebot, Elphias Doge, Dedalus Diggle, etc.
Hermione Granger - She's on the borderline between possible and likely. She's made a few powerful enemies (Umbridge and Skeeter) and offended two categories of magical creature (Centaurs, House Elves). She's often broken rules where it suits her and has yet to pay a price for any of it. If she doesn't get killed she will get a comeuppance from some or all of these offences.
Ron Weasley - possible only because of the symbolic sacrifice in the wizard's chess game in Sorcerer's Stone. I think if Hemione dies, so does Ron. If she lives, he lives.
Another Weasley - A Weasley has been in mortal danger in every single book. They may not dodge the bullet a seventh time. On the other hand they represent the 'good' purebloods. Every pureblood family that holds the Malfoy/Black pureblood supremacy view has been essentially decimated in the books, so the Weasley's with their more progressive views might well be spared.
Neville Longbottom - He will do battle with Bellatrix and may not survive, and I believe he will be present at the final battle putting him in jeopardy. He is also a pureblood of the progressive bent and may be spared. These progressive types might be spared because they will have to rebuild the Wizarding World after Voldemort's defeat.
A Hogwarts Professor (Other than Hagrid) - I think McGonangall, Flitwick or Slughorn could be killed. Again to establish the gravity of the war.
Harry will definitely survive.
That's about all I have to say on this, and we'll have all the answers we want on Saturday.