As we all know that Voldemort had one of his Horcruxes in as Harry himself, but sighting that he would be defeated at the hands of Harry, why didn't he - the Dark Lord - take a look into the future to know what was to happen. He could trace down Harry's Muggle residence and try to kill him altogether. That would have given a twist to the story, wouldn't it?
For a start, Harry was protected from Voldemort through ancient and powerful magic while he remained at Privet Drive. That's why the Death Eaters had to wait until he left Privet Drive for the very last time to attack him, they couldn't do it while he still called it home.
As for looking into the future, I don't quite understand how he's supposed to do that. Divination is a very imprecise branch of magic, and actual prophecies are rare and (as far as I know) can't be produced at will. And, while prophecies certainly do exist and come true, there's some evidence that even very skilled witches and wizards (Professors Dumbledore and McGonagall, to name two) think Divination is, on the whole, a complete farce.
The most powerful spell in this world of wizardry is that of LOVE, as stated by Albus Dumbledore. This magic spell of love was cast on that very day when Harry's mother Lily gave her life in order to protect him from Voldemort. Lily's blood ran through her sibling Petunia and that magic was there in Pivet Drive where she resided.
Thus, no harm could be done if Harry stayed with Durseleys until he turned 17 (that's when you become an adult in the wizardry world) and that's when the spell broke.
Even Dumbledore had cast a spell so that no matter what, Harry always manages to get a room for himself in the Durselys' Residence.
Well, the Dark Lord 'looked into the future' through the prophecy as reported by Severus Snape. Now, wait for it; yes, now comes the real thing about a twist; on hearing the prophecy, had Voldemort chosen Longbottom, (he was another option wasn't he?) the story would have been
"Neville Longbottom and the Sorceror's Stone"
and so on. Every thing has an explanation in the last book on Deathly Hallows. Well, the last book might just have been named
'HP and Clearance of Doubts: Uncovering all Secrets'!
Because his mother died to protect him and 'while he could call home the place where her blood (petunia) lived, Voldemort could not touch him there because Voldemort had shed her blood' when he killed her, even though technically he didn't shed her blood he just AK her. At the person who said if Voldemort had chosen Neville, it would be Neville and the Sorcerer's Stone, no it wouldn't. If Voldemort had chosen Neville then Neville and his parents would all be dead. REMEMBER. The ONLY reason Harry survived was because Snape begged Voldemort to spare Lily. Voldemort was going to kill them all, but Snape begged him to spare her because he loved her, and Voldemort agreed because Snape had told him about the prophecy. This was the only reason Harry survived. Lily didn't have to die, she begged Voldemort to kill her instead, and to leave Harry alone. She sacrificed herself. Neville on the other hand. Voldemort would have had no reason to spare either of his parents.
If Voldemort could easily look into the future, he would have never bothered having his gang retrieve the prophecy. I don't think the books imply at any point that he himself had any prophetic powers.
Well, Deathly Hallows makes it pretty clear that Lily's sacrifice kept Harry hidden from Voldemort- the Death Eaters knew the general area, but were unable to find the house.
Also, user32074, Neville's parents might have saved him. It's impossible to know.
The Dark Lord knew it was too well protected.
The Dark Lord knew that Harry was protected at the Dursleys’ by the charm Dumbledore used, and knew that the charm made it impossible for him to get at Harry while he was there.
“But how to get at Harry Potter? For he has been better protected than I think even he knows, protected in ways devised by Dumbledore long ago, when it fell to him to arrange the boy’s future. Dumbledore invoked an ancient magic, to ensure the boy’s protection as long as he is in his relations’ care. Not even I can touch him there.”
- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)
Knowing where his Muggle residence was wasn’t the problem - the Dark Lord knew it was impossible to do anything to Harry there.