Not as dramatic as some others, but earlier in the year I had an AUS-DFW-BOS flight with a 40min connection in DFW. Normally I'd prefer a longer connection, but this ticket was paid by a 3rd party and I was stuck with what I was given.
Plane from Austin got to the gate a little late, but since DFW has an airside connection, I was pretty confident I would make it.
Incoming flight landed at Terminal C, got on the Skylink and headed for Terminal A where my connecting flight left from... but once we got to the first Terminal A station, the doors wouldn't stay shut. An announcement came through saying the Skytrain will be stopped here for maintenance and with only 20min to go for the connection, I needed to run for it.
Managed to make it to the other end of Terminal A when general boarding started (missed my Group 4 boarding), but it wasn't all too bad in the end since I was greeted with a totally empty row 22 and 23, had my choice of seat, and the FAs gave me some extra cookies on top.

For a stars totally aligned flight...
BOS-CLT-AUS leg, plane from Boston took off early and landed early in Charlotte, incoming gate was the same as the outgoing gate. I pretty much walked off, then walked back on the same plane an hour later, back into the same seat even.