Depends entirely on concentration, but it doesnt do what is displayed in the movies. Breathing though a chloroform soaked rag might put you out in tens of seconds.
If you just sniff the bottle, nothing will happen in terms of passing out or even getting dizzy, but the headache after a while surely is a true thing. I have worked in chloroform and methanol/chloroform mixtures in the lab often enough. Even if you dont work in a fumehood (which you should) the vapour from a couple of open vials don't do anything but smell bad.
Chloroform, and more notably, ether, were used as aneasthetics in the distant past, but that required continous breathing of pretty high concentrations. They were abandoned because of health problems for the patients (and fire hazards with ether), but keep in mind that back in those days, the doctors were working on a patient that exhaled the stuff right into the operation area, without much ill effect to them.