If I am going to be spending any amount of time under the car, I have multiple jack stands PLUS I have the jack lightly pressed against the lift point. IE - I lift the car with the jack, put jack stands in place, lower the car onto jack stands, once the jack has left a gap with the lift point, I re-raise it to the lift point without actually applying more lift.
Thus, I have 3 points of failure before the car comes crashing down. To be honest, for the most part, I trust the jack more, but for safety, I place jack stands when I am going to spending time there. Wife walks by and bumps the jack handle? No problem. (Granted, she'd never do that, but that's probably the biggest fear as I am not lifting heavy vehicles by any means.)