I guess my two best are...
1.) BHM to MCO (fine fine, Birmingham to Orlando) one late spring evening on a Friday to go to Florida to relax for a weekend
It was a normal flight until we started moving into the Florida peninsula, and the whole thing was lit up by massive lightning storms and clouds blocked any views. We approached down to Orlando, and the pilot informed us we didn't have ground clearance for Orlando on account of a squall line, so we were going to have to wait it out for a few in the air. "A few" turned into 20 minutes, then into 40 minutes, but in the middle somewhere Mr. Pilot told us, "So things are still patchy down there; if we do not have clearance soon, we are going to have to divert to Tampa to stop-over, refuel, and then quickly make the trek back to Orlando."
So, finally, about 45 minutes of hanging later, we start to make an approach... Before we do, though, Mr. Pilot comes out again and says, "Alright, folks, we're first in line for an Orlando landing when this opens up in a few minutes, and we're going to give it one shot, and, after that, it's straight to Tampa, and we're landing there no matter what as quickly a we can." He kind of slipped at the end there, by implication--that is, we're *really* low on fuel, and conditions in Tampa aren't much better, so we're going to give this one try, and if that doesn't work, Tampa is basically a de facto emergency landing that we have to stick no matter the conditions on fuel concerns. I had a wifi up on a radar app to see that was the issue the whole time, and, well, both looked bad, and Jacksonville/Ft. Meyes/PCB/Miami were far away and looking like they had their own problems. It was a bumpy, wet one to say the least. Never a moment I was really in my seat, and I didn't see the ground on account of clouds and rain until we practically smacked into it.
We made it, but I wondered how long it was going to be until we were gliding.
2.) ORD to DCA (again, Chicago-O'Hare to Washington-National)
I was coming back from, I think, Calgary to Washington, and had a late flight out of O'Hare on a United 757 (I think) back to National. It was another one of those dark, windy, spooky nights you get in Washington in the late winter, and we approached DCA from the north on the "river visual" pattern (following the black ribbon of the Potomac, with the empty space for Arlington National Cemetery with no lights off to the right). It was incredibly turbulent--I've had roller coasters that treated me more gently by a wide margin. Up, down, left right, up, down, down, down, left, right, up, etc. We got close the first time, didn't seem to have the right angle, and I could hear the engines throttle up, and then we came back around and did the same thing with the same results.
The captain came on, "Sorry, folks, but the weather here and the tight approach is making this really difficult. We're going to give it one more shot, but then we're going to have to go to Dulles and touch down to hunker down for the night." So, we give it one more go, and it's the same results in terms of movement and bucking, but, by the end, we hit the ground hard and the pilot sticks the thing. Once we are slow, taxiing over the tarmac, he comes back on, "People, I've been doing this almost forty years, and I few F-4s over Hanoi back in Vietnam. I have never had a harder or a rougher approach or landing in my entire career than what we all just went through. Thanks everybody for sticking with me through it, and I'm glad we got you home without having to go to Dulles or Baltimore, where it would still have been bad but at least we'd have more space to work with." ~or something to that effect, particularly the bold material