I used to hear this all the time when I was growing up. Just ignore bees, don't swat at or try to kill them, because if they die, they'll send a "signal" to the hive that will attract dozens more. After forgetting about it for many years, I recently heard the same claim from adults.
I've killed and seen killed several bees and haven't been subsequently visited or attacked by swarms the size of a grand piano, but maybe they were just very far away from their hive.
There's all sorts of anecdotal/non-credible mentions of this claim, but I've never seen anything convincing. For example, from an exterminator's site:
Do not swat at bees. Swatting bees causes the release of an alarm signal and only increases the intensity of an attack by stimulating other bees to attack
Or from a September 1988 issue of Field and Stream:
Don't kill bees. Injured or dying bees are thought to emit a cry of distress, which other bees respond to quickly. The alarm signal sends squadrons of armed investigators to the scene. These rescuers often attack anything that moves or that has body temperature.
Final example from this Associated Content article, which references a semi-trustworthy government source but it is not clear where this specific claim was derived from:
To avoid getting attacked by bees, one should never swat or threaten a bee. The reason for some swarm of bee attacks are due to the release of a pheromone a threatened bee will emit. This pheromone sends a distress signal to all other bees in the area, and will attract the whole swarm to come in and defend them.
It mentions a pheromone being responsible, but the government source, quoting another primary source, only seems to talk about this in the context of colony defense, and if I'm reading it correctly, releasing the pheromone is only really effective in proximity to the hive and is also one of the first things a defender does (long before one would have a chance to swat).
Is there any truth to the claim of dead/dying bees sending off an "alarm signal"? Is it backed by research, or is it just an old wives' tail?