What the most impressive/lucky/awe-inspiring ways your Kerbals have pulls victory from the jaws of defeat?
One of mine was a harrowing re-entry with a beleaguered SSTO in a modded save awhile back. At the time there was an issue with Infernal Robotics that would cause FUN! to happen if you attached a docking port to a I.R. part. An issue I was unaware of.
WARNING: Wall of text incoming!
In my blissful ignorance I put a docking port on the end of a segmented, actuated arm in the cargobay of my SSTO, the Charon, and launched her on a taxi mission to my LKO science station to rotate my scientists. Jeb was at the wheel, so what could go wrong? The ascent, rendezvous, and docking went off without a hitch. The new scientist boarded the station, and Bob settled into the Charon to take some R&R before his deployment on the soon-to-be-launched manned Duna mission. The undocking went as planned as well; it wasn't until I tried to retract the docking arm and found that it was frozen in place that I realized something had gone amiss. The cargobay doors proved similarly unresponsive. Now this was my "no quickload no respawn" career save, so I had to live with the mechanical failure. Worse, I had Deadly Re-entry and FAR installed, so even though vanilla heat mechanics weren't a thing, death due to bad re-entry was a very real threat. Still, only the docking arm was new; the Charon's airframe was a design I had flown and landed probably fifty times at that point. I was confident I could bring her down safely. I burned for reentry and dropped to into the atmosphere.
The Charon's aerodynamic profile was seriously compromised thanks to the docking port; the first hints of drag immediately tried to pull her off vector. Still confident, I tried to compensate, only to instantly and completely lose control. Everything I did only seemed to make it worse. Strain on the Charon's frame was increasing. I tried to reign her in hard, and instead flipped her clean over in the opposite direction. With the spaceplan wrongside up, a combination Deadly Reentry and FAR disassembly began their work. Parts started coming off like waterdroplets on a windshield. Every battery, antenna, mechjeb component, and parachute was scoured from the cargobay and upper hull. Finally the docking arm and the outer winglets were sheared/burned off, with part of the debris taking one of the tailfins as it went. The end appeared nigh.
Without the drag from the arm, the plane became a bit more conventionally aerodynamic and righted herself before Deadly Re-entry could live up to it's name. Less fortunately, the chaotic descent had dumped more speed than expected. Where the original flight plan had put the Charon above the KSC, she was now falling into the mountains to the West. As a final nail in an already well secured coffin, the plane had traded the crazy rolling of re-entry for a rotating pancake drop. It was more genteel, but no less lethal. The worst part was that the control surfaces appeared to be functioning, but the plane itself wasn't responding as expected. I was bewildered. Jeb and Bob were going to die a scant few kilometers from home, and there was nothing I could do about it. Then I looked closely and the Charon's wingtips and the full extent of what the Infernal Robotics bug had done to me was made clear.
The bug hadn't just frozen every actuator on the ship, it had inverted every control surface as well. (While leaving the reaction wheels alone.)
With this newfound understanding (and after some desperate attempts to click spinning parts in order to disable the reaction wheels) I slammed the Charon into a nosedive. The spinning began to slow, but I still lacked the airspeed to maintain flight. The plane dropped below the peaks of the mountains, still mostly in free-fall. Ground clutter had just become visible when the Charon was finally able to pull up her nose and gain horizontal momentum. I even managed to limp my way over to the KSC and landed on the runway, though the Charon was burned, bruised, missing more than few parts, and decidedly worse for wear.
I had to take a break after that one, my hands were shaking.
So yeah, that's my closest call. What have your Kerbals barely survived?