Intent (or "mens rea"), not motive. Some killers don't have a motive; see the Louisiana murderer who confessed to killing a child who came to his door to sell candy -- he confessed, saying only that he "had a bad day." Motives are used to explain why the accused might have done something, but aren't necessary for the legal definition of a crime.
In some cases, murder does not require mens rea, when the accused shows "extreme indifference to the value of human life" (e.g, "depraved heart" manslaughter). The classic legal example is someone who sits at the top of a skyscraper idly tossing bricks off the side; they might not intend to kill someone, but their callous and wanton disregard for human life means that in most jurisdictions they're going down for murder.
Murder always requires mens rea. Crimes that do not require mens rea are called "strict liability crimes" but murder is definitely never one of those.
>In some cases, murder does not require mens rea, when the accused shows "extreme indifference to the value of human life"
In such a case, the extreme indifference IS the mens rea. The prosecution must prove the existence of that extreme indifference. Murder without mens rea would mean that the prosecution wouldn't need to even discuss indifference.
In some cases, murder does not require mens rea, when the accused shows "extreme indifference to the value of human life" (e.g, "depraved heart" manslaughter). The classic legal example is someone who sits at the top of a skyscraper idly tossing bricks off the side; they might not intend to kill someone, but their callous and wanton disregard for human life means that in most jurisdictions they're going down for murder.