I once got to the gate at DTW after sitting on the ground at HPN way too long before we took off. I ran like mad, arrived within 10 minutes, but they'd locked the door. No denied boarding compensation- you just get put on the next flight that's convenient for them.

I'm also cautious about tight connections and book long layovers to be safe- but then half the time they change the schedule on me, for the worse. Usually the new layover is unacceptably short (and I once called and got that changed) but when we went to Alaska the 3-hour layover I'd scheduled was changed to 7- and with a delay it became 8. We bought day passes for the lounge but I hated giving UA more money for messing up our schedule.