I feel there are two reasons Roy saved Deckard.
The first is that, during his final moments, Roy utters his awesome "Tears in the Rain" soliloquy, which extols the wonders of life, and despite its complexity, how utterly fleeting and transitory life is:
I've seen things you people wouldn't believe. Attack ships on fire off the shoulder of Orion. I watched c-beams glitter in the dark near Tannhäuser Gate. All those moments will be lost in time, like tears in rain. [pause] Time to die.
Rutger Hauer, the actor playing Roy Batty, improvised that speech a bit at the last moment, cutting some of the scripted speech, and adding a bit of his own improv.
In interview with Dan Jolin, Hauer said that these final lines showed that Batty wanted to "make his mark on existence ... the robot in the final scene, by dying, shows Deckard what a real man is made of." from The Ridley Scott Encyclopedia.
Roy Batty, throughout the final confrontation, points out Deckard's failings. He breaks his fingers for Pris and Zhora, and asks Deckard "proud of yourself, little man?". He directly taunts Deckard's supposed moral highground: "Not very sporting to fire on an unarmed opponent. I thought you were supposed to be good. Aren't you the 'good' man? C'mon, Deckard. Show me what you're made of."
The first, and most obvious reason Batty spared Deckard's life is to demonstrate that he (Batty) understood the value of life, and what it meant to be "good", better than Deckard, the supposed protagonist of the story. It is one of those moments that flips the perspective of the entire narrative, and suddenly the "bad guy" is now the sympathetic victim of a system that never gave him a chance. It is, in my opinion, one of the single greatest moments in the movie, and is one of the primary reasons why I consider it a true classic.
The second reason is more subtle, and more speculative.
The original version was "lightened up" a bit by the studios. Changes made in the later Director's Cut, however, introduced hints that Deckard himself might be a replicant (the "unicorn scene", and Gaff's unicorn origami). During an interview in the 2000 BBC documentary On the Edge of 'Blade Runner', Ridley Scott confirmed that Deckard is, in fact, intended to be a replicant.
In the light of this revelation, it is conceivable that Batty knows this, and saves Deckard out of a sense of kinship (which also ties in with the moral high ground portion above).