Are there any airlines that still allow smoking on board?

Actually, yes there are.

Much of the world does not have strict regulations about smoking onboard, and in much of Europe it is the carrier's decision to allow smoking or not. A new German carrier called Smintair (Smoker's International Airways) currently has plans to start smoker-friendly flights between Europe and Asia on a 747 specially outfitted for high-paying smokers who wish to indulge their nicotine addiction on the flight.

Other middle eastern and Asian carriers permit smoking onboard, but I do not have a complete list of which ones. In all of the United States and much of Europe though, smoking has been banned for some time now.

Commercial airlines do not. As far as those private company jets they can make their own rules so they could permit smoking. I bet that when the head of Philip Morris flies on the corporate humongous plane that the flight attendants don't tell him "Federal regulations prohibit smoking on this flight."

No, yet they continue saying "this is a non-smoking flight..." as if there actually are some flights where everybody sits smoking a stogy from take-off to touch-down... Imagine how full of smoke the plain would be! the pilot won't be able to see the controls in the cockpit!

Not only is smoking a fire hazard, it is bad for everyone on board... also, it would require a lighter, and those are banned by TSA. Finally, it takes away from the cabin's life, the seats must be replaced sooner once they become saturated with smoke...

No and it's too bad, why not have the special seats for smokers as it used to be or why not have a special room for smoking. This is simply fundamentalism and it's spreading.

Some (very few) European charter companies still allow smoking!

No commercial airlines in any country.