As a non-rev passenger I never counted on actually being able to board the particular flight I wanted. But I did have the advantage of being able to check on the computer to see whether the flight was sold out, the extent to which it was oversold (usually 110% for coach), and how many people were ahead of me on the standby list. So if all the seats were sold and there were people ahead of you on the standby list, you could conclude your chances weren't good. The only thing you couldn't know for sure was how many no-shows there would be. But if everybody who bought a ticket showed up, the extra passengers would have to be accommodated (bought off); the plane would be full and there would be no room at all for the non-revs. If there were more no-shows than expected and there was an empty seat or two, the people at the head of the standby list would get seats, but if you were farther down you'd just have to wait for the next flight, or figure out a route involving a stop or two. Guy I knew made the mistake of trying to non-rev around Christmas, tried to get home from somewhere in California, got as far as MEM and discovered the only way back to MSP was via DTW and then AMS. He managed to get to Des Moines and then rented a car...
Or sometimes the passenger list looked like there were enough seats but something else would come up, like weather. One time I waited around to be called and the gate agent started asking for volunteers to give up their seats (I don't remember what they were offering as an incentive) because the plane was overweight. It wouldn't have been overweight except for the fact that the weather suddenly took a turn for the worse at the destination and they had to board more fuel in case they needed to hold or divert. So I was out of luck.
I never saw anybody involuntarily removed from an airplane. Seems like whatever they were buying people off with did the trick.