Last year on an ORD->OMA UA flight we were delayed an hour, then it was announced that the DSM flight was cancelled for mechanical reasons and those pax would be boarded onto our flight. It's amazing how without reissuing seats, the OMA pax were all in the back of the plane and the DSM ones all in the front. I think I arrived in OMA like 15 minutes before the Avis desk closed. Had I missed that I might have been mad.

Within reason (like 20 minutes or so), I don't mind holding flights for connecting pax or situations like this because I hate being stranded.