Is it possible to overdose on nicotine from cigarettes? How many cigarettes would one have to smoke to reach this point?
Just crunching the numbers, it at least seems unlikely.
The lethal dose of nicotine is often stated to be around 50 to 60 milligrams, though it might be higher, with more recent data putting it closer to 500.
Smoking a cigarette takes several minutes, let's say 3. The lowest lethal dose estimates I could find were 30 milligrams; smoking 30 cigarettes, for ingesting 30 milligrams of nicotine, would then take 90 minutes, at which point the body has already gotten rid of some of the nicotine.
Even at the very conservative estimate of 30 milligrams as a lethal, or at least toxic, dose, smoking likely won't get you there, unless doing it competitively for hours. Even for smoking cigarettes at the same time as using nicotine patches (OCT NRT) the FDA states
There are no significant safety concerns associated with using more than one OTC NRT at the same time, or using an OTC NRT at the same time as another nicotine-containing product—including a cigarette.
Eating cigarettes or drinking e-cigarette liquid are different stories, though. That's usually the scenarios in which nicotine overdoses occur.
As always, this is not medical advice. Please don't try to smoke 60 cigarettes an hour. It's not healthy either way.