Just finished the final book last night. I understand that (spoilers)
Snape was a double-agent spy for Dumbledore, but what usefulness did he bring? What information did Snape bring to Dumbledore about Voldemort or his Death Eaters?
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While answers involving the information disseminated by Snape are technically correct, there are strategic aspects involved in choosing Snape for his role which reflect on Dumbledore's intelligence and his disbelief that Voldemort was truly eliminated.
Prior to the resurgence of V. and the Death Eaters, it would still have been valuable to have someone monitoring talented Slytherins and guiding them in a manner that prevented them from becoming the Wizard version of an ISIS recruitment center that they became once the DE's returned to power. The choice of even educating Slytherin house as happens at Hogwarts (whereas the other schools appear to have a single unified house throughout the series, per school) is pretty dubious. After V's original rise to power, the only reason to continue to educate in this manner would be to identify potential problems, which would make a talented Death Eater-turned-traitor an ideal monitor for such a program. Slytherin house only makes sense as a bad-kid-monitoring program.
Snape knew how wands worked. The delaying actions that eventually resulted in Snape's death at Voldemort's hand prevented the Hallows wand's use as a weapon until its ownership had been heavily muddled. Considering its capabilities, this may have been a key point in deciding the outcome of the war.
Snape was the only person alive who had such a heavy emotional investment in Harry that he didn't need to be given specific orders in order to defend him. Snape's own motivations would not only prevent the security weakness of having to communicate intent to a spy from the controller, but it would also ensure Snape's loyalty as the situation grew darker.
Manipulatively, Snape was an ideal distraction. Countless times, focus on Snape as a potential source of evil intent kept students out of the way of the actual danger, and his very presence prevented the children from ever lowering their guard, which is exactly how Dumbledore wanted them. Their suspicion of Snape was repeatedly a vehicle by which a true evil was uncovered; without him, the Quirrell plan would probably have been all that was necessary to topple potential resistance to Voldemort's return.
Voldemort didn't return and summon the Death Eaters until after the events of "The Goblet of Fire." Prior to this, Snape would have only been observing Slytherin house and, potentially, any stray Death Eaters who would associate with him after Voldemort fell in Godric's hallow. Dumbledore was suspicious that the Dark Lord had not been fully destroyed, so Snape's role during this time was to watch for signs of his return and monitor the remnants of the Death eaters.
After Voldemort's return, one sure piece of information which passed from Snape to Dumbledore was the plot to have a student kill Dumbledore. Information on plots and the Death Eaters in attendance would surely be gained from the Death eater meetings which Snape attended; However, the books do not specifically mention this information being passed down.