I was driving an old work van on the highway, doing the speed limit of 65 mph (105 kph). As i crested the hill traffic was stopped a few hundred yards ahead. I had plenty of room to brake and come to a stop, a bit abrupt for the weight of the vehicle but no big deal. I applied the brakes and the pedal went right to the floor. The brake lines had blown out from corrosion. I was in the right lane and there was an exit ramp to my right. The stopped traffic was fast approaching. I dropped the automatic transmission into low gear (it was an older Chevy, so it had R N D 4 3 2 on the column) and swerved right, with what felt like a fraction of an inch to spare from the car in front of me. I swear I could see the sour expression of a woman who very nearly has her day ruined go by in slow motion, like that Umbrella Academy meme. The off ramp gave me time to pump the brakes and let the engine slow the vehicle down. I was fully prepared to throw it into park if necessary, but by the time I got to the intersection enough brake pressure had been regained to stop. Pulled off the road and had that POS towed to a garage.

There was the time I high-sided my motorcycle, but OP asked for almost, not actual.