Over many traveling years just a handful of out of the ordinary incidents come to mind - with only the first listed below even coming close to "seconds from disaster".

1) Flying SCL to EZE on Brazil's flag carrier VARIG we encountered windshear just after crossing the airport perimeter at Buenos Aires. The flight crew aborted the landing and we ended up diverting - first option was Montevideo but that was discarded due to weather and we ended up in Porto Alegre, Brazil. Where I had my first, and hopefully only, experience as an illegal alien (no Brasilian visa) in Brazil (you can find this story by searching old Trip Reports). It's pretty scary sitting at the window, moments from landing, when you hit windshear and the ground is coming up a whole lot faster than usual all at once

2) ORD to SMF on UA - diverted to SLC en route due to a problem with the oxygen supply to the flight deck. Made for some interesting channel 9 listening as our crew checked in with ATC to find out just how low we could safely fly in the area without running into any mountains. At SLC mechanics fixed the problem and we were underway again inside of 90 minutes.

3) SFO to SMF on United Express - returned to SFO after departure due to inability to retract one of the landing gear. Of course this is much more preferred than not being able to deploy the landing gear!

And a friend of mine was once flying SMF-DEN on UA that diverted to RNO not too long after departure. Seems that the aircraft couldn't maintain cabin pressure and the O2 masks eventually deployed. He told me it wasn't too big a deal, everybody put on their masks - he confirmed that yes, they do work and no, the bag does not inflate. They only had to wear them a very short time as they were nowhere near their final assigned altitude and it was a quick trip down to a breathable altitude then expedited approach into RNO.