Two experiences of mine: Braking on snowy/icy streets.

First, in a car without ABS, I put on the brakes (I was probably going a little too fast) to avoid hitting the car stopped ahead of me. I started to slow down, but also to slip to the right towards the curb; it was scary, and I barely slowed down in time to avoid either collision.

Second, in a car with ABS, I slowed down to turn into a parking lot, and the ABS kicked in; the car went absolutely straight (without slowing down enough to make the turn), but I wasn't sliding at all, so I didn't have to worry about sliding into the curb. Big win.