Voldemort killed them with the Avada Kedavra. I thought everyone knew that. He killed them, trying to get to Harry, and the Killing Curse reflected off of Harry because of his mother's love and hit Voldey. Come ON!!! I'd tell you more, but that'd be a spoiler.
You got it all wrong, folks. It's Santa Claus that killed James and Lily. He wanted to give gifts to Harry but when reminded this was only Halloween and not Christmas, well, he got kinda pissed off.