Why doesn't a cigarette lighter generate thrust? The way thrust is created by a rocket is discussed here: How does fire create thrust in rocket?
If you look at a typical rocket, say V2, it has two primary tanks — one which stores the fuel and the other which stores oxygen. Is it that the lighter flame doesn't use its own oxygen, the reason that it doesn't generate thrust? Or is it that the thrust is so small that I can't feel it? Or is it something more complicated like the shape of the nozzle?
 A: Thrust is the reaction force derived from a rocket nozzle. You don't have to have combustion or fire to create thrust as evidenced by simple soda bottle rockets that use water and compressed gas. But in spaceflight combustion is one of the more efficient ways to create thrust in terms of the energy produced and weight of material required to derive that energy.
The force of thrust is derived by momentum exchange. The rocket throws off many small particles of mass at high velocity in one direction and by Newton's third and second laws, the spacecraft is accelerated in the opposite direction.
For fuels that do combust, a thrust chamber is engineered which allows the combustion to build a high pressure, and at one end of the chamber a nozzle is fitted that retains the chamber pressure and increases the velocity of the thrust. The magnitude of the thrust force is roughly the chamber pressure times the nozzle cross sectional area.
For the butane lighter there is no thrust chamber, and the combustion takes place in the atmosphere where pressure can't really build up. If there is any thrust to consider it only comes from the expansion of the butane gas from the valve opening, before combustion takes place. And I'll wager its on the order of micro-Newtons.
A: For the average disposable lighter, when you press the fuel lever a pressurised liquefied gas is released which will create a very small thrust.
The combustion, however, will not generate thrust because, unlike a rocket engine, it is not occurring within a chamber.
A: Newtons third law states that every action has an equal and opposite reaction.
A cigarette lighter is venting gas from a pressurised container and igniting it. The act of venting upwards will create a small opposing downward force.
Additionally, the ignition of the vented gas by the striker wheel creates a small pressure wave in the air, similar in principle to the shockwave that precedes a bullet or supersonic aircraft. (You can actually feel this force on you finger as you strike the lighter.) This pressurewave can be photographed with a high-speed camera - I'm not sure if anyone has done it with a lighter but there are videos on youtube of bursting balloons and targets being shot with bullets, filmed at 100+ frames per second, which illustrate this principle nicely.
In other words Cigarette Lighters DO generate thrust, it's just an almost imperceptibly small amount of thrust.
