Airbags are safe for the intended target person but can be dangerous for others, such as infants and children.
There have been over 800,000 air bag deployments, saving over 1,500
lives. To date, completed investigations of air bag crashes show that
many of the air bag injuries were due to the driver sitting too close
to the air bag module or passengers riding unbuckled or incorrectly
secured. The latter includes infants in rear-facing child safety seats
that are placed in the front seat or small children incorrectly placed
in a lap/shoulder safety belt.
Air bags save lives. Air bags in passenger cars and light trucks
prevented an estimated 1,136 fatalities from 1986 to 1995, with
another 600 saved in 1996. Once these life saving devices are equipped
in all cars, it is estimated that 3,000 lives will be saved each year.
Driver-Side Air Bags Driver-side air bags reduce the overall fatality
risk of car drivers by a statistically significant 11 percent.
In other words, a fleet of cars equipped with driver-side air bags
will have 11 percent fewer driver fatalities than the same cars would
have had if they did not have air bags. Still, air bags can be
dangerous to short stature adults sitting too close to the air bag
module, especially when unbuckled.
Passenger-Side Air Bags Passenger-side air bags reduce the overall
fatality risk of car passengers age 13 and older by a statistically
significant 13.5 percent.
It is estimated that an additional 88 right front passengers ages 13
and older would have died from 1986 to 1995 if passenger cars or light
trucks had not been equipped with passenger-side air bags.
To date only one passenger, a 98-year-old female, has died as the
result of an adult passenger-side air bag-related injury.
Taken from here, which reports the NHTSA as its source for these claims, though I found the NHTSA site a bit difficult to navigate to find anything like this. I am not sure whether the to date part means some time in 1995/96 or more recently, the updated date did not cite a year and the latest copyright date was 2004.
I would assume that these numbers have gotten better in recent years simply due to better airbag technology (like cars that automatically disable airbags based on weight) and awareness of proper usage and precautions.