It's possible for a motorist who accidentally causes the death of another person to be convicted of murder. However, fatal accidents usually don't lead to murder charges—much more common are lesser charges like vehicular homicide (also called "vehicular manslaughter) and involuntary manslaughter (sometimes referred to as "second-degree manslaughter").
State murder laws vary. But if a motorist is charged with murder for accidentally killing someone while driving, it'll typically be second-degree rather than first-degree murder. Generally, to be convicted of first-degree murder, there needs to be proof that the perpetrator intended to kill the victim.
Though second-degree murders involve accidental killings, the crime can still be hard to prove. In most states, the prosecution must establish not only that the defendant did something extremely dangerous to human life, but also that the defendant was aware of the dangerousness prior to acting. In terms of driving-related cases, second-degree murder charges are most common in situations where the defendant's driving obviously posed a substantial risk to the lives of others or there are other facts showing the defendant knew the driving was unsafe.
Example: Erik just bought a new Camaro. To celebrate, he drove down to his local tavern. After several shots of vodka, Erik decided he was ready to see just how fast his new car could go. Erik remembered learning about the dangers of drunk driving when he participated in an alcohol education program as part of his probation for a prior DUI conviction. But he figured everything should be fine since his Camaro had excellent brakes. Unfortunately, Erik got carried away—as he broke 120 miles per hour around a curve in a residential neighborhood, he lost control and ran into a pedestrian. The pedestrian died instantly. A jury might convict Erik of second-degree murder because his driving was egregiously dangerous and he had reason to know of the risks associated with his conduct.
Most states have laws that specifically apply to situations where someone accidentally kills another person while driving. States use various terms for the offense, "vehicular homicide" and "vehicular manslaughter" being the most common. But drivers can generally be convicted of this offense only if negligent or culpable in some way. In other words, pure accidents where the driver wasn't at fault for doing something wrong aren't crimes.
In other states, more general manslaughter laws cover accidental killings that occur on or off the roadway. In other words, there aren't vehicular homicide laws that apply only to driving-related killings.