The Blacks:

What happened to Sirius' two-way mirror? How will it play a role?
What is Regulus Black's middle name? Will he become important? - DT
Will we / how will we see Sirius again?

Creatures:

Will Norbert return?
Will the house-elves ever stand up for themselves / will Hermione's efforts on their welfare be wasted?
How did Fawkes' phoenix feathers come to be used by Ollivander?
Where's Fawkes? Who owns him now? - Marty Forsythe
How is it that the house elves can Disapparate within Hogwarts? What sort of magical powers do they possess that wizards do not? - Scott
Why is Neville's toad always trying to escape Hogwarts? - Shelley

Dumbledore:

Why did Dumbledore trust Snape?
How and why did Dumbledore learn about Horcruxes in the first place? - Taryn
Will Dumbledore's portrait play a role? - Marty Forsythe
Why did Dumbledore have James's invisibility cloak? - Karl
Was Dumbledore an Animagus? - Karl
What was contained in the other letters Dumbledore and Petunia wrote to each other?
How does Dumbledore's family play into the last book?
What is Aberforth Dumbledore's role in the Order of the Phoenix, and what will it be in the final resolution?
What did the potion in the cave do to Dumbledore?
Was Dumbledore going to die anyway, because of the potion?
What was Dumbledore seeing when he drank that potion? - Sara Hughes
What did Dumbledore really see in the Mirror of Erised? - Kellie
How did Dumbledore understand Morfin and Marvolo when they were speaking Parseltongue? Is he a Parselmouth? - Sharbani
Did Dumbledore leave a will? - Sarah
Why did Dumbledore choose to name his anti-Voldemort group The Order of the Phoenix? Has it got something to do with Fawkes? - Mariya
Upon learning that Voldemort had used Harry's blood to restore himself to his own body, Harry notices that Dumbledore has a "gleam of triumph" in his eyes. Why?
Dumbledore knew that the Defense Against the Dark Arts job had been jinxed by Voldemort, so why did he allow Snape to finally take the position in Book Six? - Sariti1214
What was Dumbledore asking of Snape when he said “Severus, please” on the tower? - DT
What will happen to the memories Dumbledore was storing in bottles and in the pensieve? Who will inherit them, and will they be of any use since he is now deceased? - Rob

The Dursleys:

What else does Petunia know about the magical world?
Who is "that awful boy" that Petunia overheard Lily talking to?
What was contained in the other letters Dumbledore and Petunia wrote to each other?
What did Dudley see when the Dementors approached?

The Longbottoms:

Is Neville Longbottom under a memory charm that's wearing off?
Where was Neville when his parents were tortured?

The Potters:

Is Harry's eye color significant in any way?
What will be the final revelation about Lily Potter?
How did Harry's family come into so much gold?
What did James and Lily do for a living?
Who else was at Godric's Hollow the night of Harry's parents's deaths?
What was Snape and Lily's relationship like?
The village that Harry's parents lived in was curiously named Godric's Hollow. Does this mean it has something to do with Godric Gryffindor? - Mariya
Under what circumstances did Lily and James defy Voldemort three times?
What is the significance of Harry's lightening-bolt-shaped scar? - DT
Will Harry ever learn Occlumency? - DT

Misc. Characters:

Will we see Viktor Krum in Bulgaria, or will he come to Western Europe?
Is Nympahdora's Muggle father Ted the newscaster from the first book?
What will happen to Draco Malfoy?
What will become of Rita Skeeter?
Who is the person who will do magic at a later-than-normal age?
What careers will the survivors of the war pursue?
Dumbledore said that Harry will be grateful one day that he had saved Peter Pettigrew. How will this come in to play? - Mariya
What happened to Ollivander and Florean Fortescue? - LiaMaria
What exactly did Mundungus steal from headquarters? Who has he sold it to? Does he still have any of it? - DT

Severus Snape:

Who is the person who loved Snape? His mother? - Karl
Is Snape loyal to Voldemort, or to the Order of the Phoenix?
When asked what Snape's patronus and boggart forms would be, JK Rowling said that she could not answer this question seeing as it would "give too much away." What are his patronus and boggart forms, then, and why are they so important? - Courtney
What story did Snape tell Dumbledore to gain his trust?

Voldemort:

Why did Voldemort give Lily the chance to live?
Who retrieved Voldemort's wand from Godric's Hollow? - Karl
Why did Voldemort and the Death Eaters go after the particular people they did in book 6 (Amelia Bones, Emmeline Vance, Hannah Abbot’s mother)? - DT
Will Voldemort know that Draco did not kill Dumbledore himself? - DT

The Weasleys:

Will Ron's scars from the brains in the Department of Mysteries have any further significance?
To whom has Percy been loyal since he split with the family?
How will Percy / will Percy redeem himself?