I don't know the exact number of actors who almost died, of course, but here are some examples.
Isla Fisher in Now You See Me:
In the film, there's a scene where Fisher is supposed to escape from a large aquarium in which she's chained.
The chain got caught in the aquarium, and she couldn't get up. Everyone thought she was giving a great performance, when in reality she was drowning. In the end, she managed to reach a quick-release fastener and free herself with the help of a stuntman.
Daniel Day Lewis in Gangs of New York
The three-time Oscar winner refused to wear anything other than period clothing.
As a result, he contracted pneumonia. When he was told he really had to stop or he would die, he finally complied.
Jason Statham in Expendables 3
The action hero was driving a truck when the brakes failed.
Statham jumped out just before the vehicle plunged 60 feet into the sea.
Jaime Alexander in Thor : The Dark World
Alexander fell down a metal staircase, causing a disc in her spine to shift, 11 vertebrae to break, her left shoulder to dislocate, and the rhomboid muscle on her left side to tear.