Voldemort offered Lily Potter mercy at Snape's request, demanding that she get out of the way so he could kill Harry. When she refused, why didn't he simply stun her or put her in a full body-bind or something like that? It seems obviously unnecessary for him to kill her; there was no clear benefit to him, and he risked alienating a loyal follower.
Which he did, because:
Severus Snape became an inside man for Dumbledore.
There are a couple of reasons:
Or maybe he killed her simply because he didn't even think of doing anything else. For Voldemort, stunning isn't really an option. It just doesn't cross his mind to stun people, especially people he has no use for.
Well we know essentially why, because we see the murder from Voldemort's own eyes.
'Not Harry, not Harry, please not Harry!'
'Stand aside, you silly girl ... stand aside, now ...'
'Not Harry, please no, take me, kill me instead -'
'This is my last warning -'
'Not Harry! Please ... have mercy ... have mercy ... Not Harry! Not Harry! Please - I'll do anything -'
'Stand aside - stand aside, girl -'
He could have forced her away from the cot, but it seemed more prudent to finish them all ...
Harry Potter and the Deathly Hallows - p.281 - Bloomsbury - Chapter 17, Bathilda's Secret
It seems really, then, that he was a killer through and through. He didn't need to kill her. But he didn't really need to kill James either, they were in the way. He would have spared her for Snape, but she defied him, she stood up to him. She tested his patience as we see here. And, after all, this was his big moment, wiping out, once and for all, the one inexplicable, great threat to him. Not a time for half-measures. A time for a show of strength surely.
While Au101's answer offers an excellent explanation, another point is this: Voldemort's concern for the wants/needs/desires of others (including Snape) is entirely utilitarian. He is only willing to accommodate their wants/needs/desires as long as he perceives a net benefit to himself from doing so.
In this situation, the liability of Lily Potter's continued life exceeded the utility of pleasing Snape by giving her to him following the deaths of James and Harry. This utilitarian view was shown in the final line quoted by Au101:
He could have forced her away from the cot, but it seemed more prudent to finish them all....
Another example of his utilitarian view of people (even of Snape!) was demonstrated by the way in which Voldemort killed Snape when it became beneficial for him to do so:
"...[I]t is of you that I wished to speak, Severus.... You have been very valuable to me. Very valuable....
"You have been a good and faithful servant, and I regret what must happen....
"The Elder Wand cannot serve me properly, Severus, because I am not its true master. The Elder Wand belongs to the wizard who killed its last owner. You killed Albus Dumbledore. While you live, Severus, the Elder Wand cannot be truly mine....
"It cannot be any other way," said Voldemort. I must master the wand, Severus. Master the wand, and I master Potter at last."
- Deathly Hallows, Chapter 32
He had already threatened to kill her and so if he did not kill her after saying he would, his reputation would be damaged. He was also aware that Lily was a member of the Order of the Phoenix and he would have seen her not only as a threat to him but an opportunity for him to damage the order and for him to stay in power.
My answer first take on this question was this--we know from the books that this spell, the killing curse, is unblockable. As far as ol' Voldie knew at the time, any other spell would have a chance of failure if she had any magical protection.
Second take is that she's an enemy and would definitely be an enemy after he killed her son. Why not eliminate an enemy when you have the chance.
Third take on it was that Avada Kedavra is actually a signature spell of Voldie's.
Fourth take is what others have already covered--he's an evil dude, and this is what he does.
As to the risk of alienating Snape, consider how close to the vest Snape played his cards--he may have asked for Voldie to spare Lily, but Voldie underestimated what effect that would have because, as we all know, he doesn't understand the power of love. The only reason why he did not kill her outright to begin with is because Snape asked. As far as V is concerned, he tried.
'Well, Severus? What message does Lord Voldemort have for me?'
'No - No message - I'm here on my own account....
'I - I come with a warning - no, a request - please....'
'What request could a Death Eater make of me?'
'The - the prophecy... the prediction... Trelawney...'
'Ah, yes,' said Dumbledore. 'How much did you relay to Lord Voldemort?'
'Everything - everything I heard!' said Snape. 'That is why - it is for that reason - he thinks it means Lily Evans!'
'The prophecy does not refer to a woman,' said Dumbledore. 'It spoke of a boy born at the end of July -'
'You know what I mean! He thinks it means her son, he is going to hunt her down - kill them all -'
'If she means so much to you,' said Dumbledore, 'surely Lord Voldemort will spare her? Could you not ask for mercy for the mother, in exchange for the son?'
'I have - I have asked him -'
As you can see from this exchange, Snape may have asked, but he certainly didn't beg--to do so would have shown his hand and make him someone that Voldie might watch in future. Judging from Snape's overall actions and words throughout all the books, especially in concern to Voldie, he KNEW what a monster he is--and he KNEW that he could only push so far without raising suspicions--plus it's likely he already had the back up plan of going to Dumbledore to get Lily protection, something he could only do if his protest was framed in a way that wasn't "weak." Likely he told Voldie that he owed her something, or that he wanted her as a plaything later, rather than that he loved her.
