When I was back in college I was late at least four or five times for Eastern and CO flights. That is what I get for relying on college "friends" to get me to the aiport an two hours away. Plus my poor time management skills did not help
Fortunately my route had flights every two-three hours throughout the day so I would just stand by for the next flight. Only once was I on the last flight of the day, not just for that airline but for the airport. I ended up sleeping in the airport and catching an early flight. Not that bad of an experience (for a college kid - would not do it now).

Recently, in the last couple months, I missed the cut off, checking in, by five minutes (short-term parking was full in DTW, had to park in outer lot). I was able to stand by for a flight 45 minutes later. I normally check in online but could not as Internet was down at my house, for the previous day.

I have never been charged a change fee.