I was on a UA flight from Reno to Denver that went through a flock of geese about takeoff at an altitude of about 50 feet. One goose went through the right engine on our 737, setting off a huge trail of fire out of the engine, and the engine made a horrible grinding sound. Seeveral passengers started screaming and it was very scary. As someone mentioned above, pilots train for one engine ops all the time, and while I didn't know it until later, the real risk was over once they got the plane to a level flying altitude.
But it was a terrifying experience-I took a bus thta night to SLC.

Planes can fly suprisingly well on one engine, as a pilot told me later, the risk with one engine is that planes don't fly on zero engines.