I only ever missed one, which really wasn't my fault, but I've made plenty that I shouldn't have.

The Bad Experience: Ryanair, London -> Vienna. Ryanair isn't a company I would ever have chosen myself, but the flights and stayover were a gift. Horrendous problems with the tube and trains meant that we arrived an hour later than we intended, but we still made it to check-in with 10 minutes to spare before it was meant to close (and about a hour before take-off). Check-in desk is lit up, the flight displayed on the screen, but no staff to be seen. My wife waited at the desk and I wandered around to locate some staff to check us in. It took me 10 minues to find a staff rep and drag them over to the check-in desk, at which point he proudly told us that we were now 2 minutes late for check-in and wouldn't be boarding. I explained that we were only late because nobody had been present at the desk, and we only had carry-on bags and 45 minutes to get through a deserted security to the gate, but they stood firm and refused to check us in. Never flown with them since.

The Good Experiences: BMI have outdone themselves several times to ensure we got connections following earlier delays, often by the skin of our teeth and by mad dashes through airports with them holding the gate open for us. Top marks go to BA though, for a trip I took London -> Manchester some 8 years or so ago, when I was so late to the London check-in that I arrived only 15 minutes before take-off, but they still checked me in, pushed me through security and onto the plane. I then managed to oversleep in Manchester the next day and made the Manchester check-in with 10 minutes to go before take-off, and they did the same thing again, smiling all the way. Hats off to the BA staff working that week.