Are we required to have one in a standard kitchen with a gas range in a residential home? The big question is not how many CFM or ducted or not, just whether there is a requirement in the building codes. I live in New Jersey, US.
Yes, and not only do you need a fan but it must exhaust outside and not just recirculate the air through a carbon filter. You are burning fossil fuels which produces carbon monoxide (among other things). This can kill you if not properly vented.
Rather than repeat what is already on this site, per the comments, see this answer for the exact code requirements for exhaust hoods.
I am sorry but I disagree with the other answers. While I would always put an exhaust over a gas range, it is not code where I am at.
Some cities require a window to be in the room if no exhaust (and room is loosely interpreted). For instance the kitchen is in the same room as dining room as long as there is no door separating the two rooms according to local inspectors.
Some allow a ceiling fan - go figure. Just saying it isn't required in most places.
Should you? Yes.
Must you? Ask building inspector.
No, it is not required or even much of a hazard to not have one. Ask yourself how often you have actually used the fan above your stove when you you had one.
Carbon monoxide detectors ARE required in most places now, that should protect you in the unlikely event you did get a significant amount accumulating in your home.