Guess: Dudley Dursley, and possibly Petunia Dursley, will be reconciled with Harry. If it's Dudley, he will have some hidden power or magical connection. They will provide a key piece of information or timely assitance to aid Harry.
This is a rehash of my incorrect book six guess. I think that these characters, particularly Dudley, need resolution. The hidden magical connection in the family is just my guess on how it will tie into the story's climax.
Guess: Grawp will take action at some pivotal moment, dimly aware of what he's doing. The dark forces will not expect this because they don't consider him an actor, being non-human.
We saw Grawp mentioned periodically throughout this book though he had no bearing on the story. Thus, I expect him to be (momentarily) significant in the final book. I'll go on a hunch and say that he will witness some confrontation and step in against a dark wizard he thinks is fighting underhanded or to step in and save Harry during some moment of physical peril (the proverbial cliff-hanger).
Guess: Dumbledore died at the end of book six. But he will return, in a different form, to guide Harry in book seven.
I'm told there's some discussion about whether he actually really truly died. I think he did. But, following the structure of the myth, he will still aid Harry in the end. Since we're in a magical world and we've seen numerous ways to interact with dead characters, I think his return will be more than just Harry recalling sage advice.
Guess: Harry will kill Voldemort. Snape, having evaded Harry, will be there to help at the critical moment and finally prove that he is on the side of good.
Voldemort dies would seem to be a "Duh!" given everything we've seen so far. Snape is really in a bad spot at the end of book six. I think he killed Dumbledore on his orders (just as Dumbledore made Harry swear to follow his commands, no matter how extreme) and will use this to get as close as possible to Voldemort. Harry will think he's fighting both of them.
Too Cool To Happen: Harry discovers that he is one of the unknown Horcruxes (something of Godric's?) used by Voldemort. He kills himself at the same time that he kills Voldemort.
This came up while Kit and I were talking. This is similar to how I wanted Lord of the Rings to end: Frodo, mortally bound and addicted to the Ring, summons just enough willpower to cast himself into the fires.
I think (because I like dark touches!) that it would be cool to see this as an ending to the Harry Potter series. I doubt this will come to pass because this is a kids' series. But it would fit all the facts, wouldn't it? :)