They will never come with bottle openers - this would encourage drinking and driving ;-)
In answer to your question, this dates back to the day when smoking was "not bad for you". Now, most car manufacturers have a "smoker's package" that is just the ash tray. The lighter socket may now have a plug to fit the opening, or may still include the lighter itself, usually, this is there only as a 12 volt power outlet, which many people find useful for other things, like charging their cell phone, a cooler etc.
Yes, they do work. I don't smoke, but I've seen people use them in the past. From what I can tell, you have to touch the end of the cigarette to the hot element inside the lighter--there is no actual flame. How does what get its name? Cigarette lighter? That seems rather obvious, doesn't it?