I had a picnic lunch with my geology class in the crater of Mt St Helens a few years ago. That was pretty neat.
I’ve handled a moon-rock at Cape Canaveral, and a gold bar from La Nuestra Senora de Atocha at the Mel Fisher Maritime Museum in Key West. (Also bought a necklace made of silver from same.)
I’ve handled some of the recovered artifacts from the Titanic.
I’ve sat in a Mercury capsuel and an Apollo capsuel, now if I can just get a Gemini.
I once spotted that a Dali painting was hung upside down in the Met but I didnt’ tell the museum, but a few days latter it was reported that they changed it.
I touched a moon rock, too, only it’s not a big deal: they have an exhibit at the National Air and Space Museum with a moon rock you can touch.
I am the youngest person to ever tend bar legally in New York State (on my 18th birthday).
I fly hot air balloons.
I have piloted an abra (water taxi) on the Dubai Creek, have opened the hatch on a Soyuz capsule and did voice-over for a mobile phone ad in the Republic of Georgia… and was reportedly the first American to cross the Turkmenistan-Iran border (according to the chief of the post on the Iran side).
I got a rock star to perform my favorite song (not a single) in concert.
(Lame, but the best I can do)
I’ve eaten at the farthest north Mexican restaurant in the world. Is that esoteric?
I’ve also steered, navigated, hauled on ropes, etc. on an authentically rigged schooner (i.e., no engine). It’s hard work. Helm is more fun than those other things because when you yell “Make ready to come about!” everybody else has to jump and do all those annoying things that you had to do when you were on bow watch. 
I ate salmon that had been caught by President Kennedy. Actually, it was probably caught by someone who was on the boat with him, but I like to think JFK caught the fish I had a bite of. (Seattle, 1962 World’s Fair, stepdad’s relatives were big shots.)
I did a temporary two week janitorial stint at Johnson-Matthey’s precious metals processing facility in Brampton. I saw rooms with wheeled tables filled collectively with several thousand pounds worth of pure gold, silver and platinum ore smelted into bricks. (I saw the smelting process, too.) I got to hold a gold brick on my first day there. It weighed about 50lbs (about 730 troy ounces) which would be worth over 700,000 at today’s gold prices. (Now imagine half a dozen carts filled with at least 20 such bricks each; that’s the room I was standing in.) He let me hold it as an example of why it would be difficult to stuff one down a pantleg and walk out with it. (Never mind the tight security measures I’d have to pass through to get it out of the building anyway.)
I used to guard President Kennedy’s grave at Arlingtion National Cemetery on the midnight shift. This was 1966, when I was with the 561st MP Company at Ft. Myer, Va.
I’ve sat, in shock, blood pouring out of my head and down my left shoulder (staining a jacket I’d eventually lose) in the ER of a hospital near Jerusalem. Very professional folks there, work like they (sadly) see that sort-of thing an awful lot.
I’ve touched a live, loaded, and mounted Minuteman III nuclear missile while on an inspection/tour of a silo near Minot, ND (I was 5 CES).
I’ve wandered through a Soviet minefield and trash dump. When the Soviets left Bagram, Afghanistan in a hurry, they buried their servicable bombs about 20-25 feet down, piled trash all over it, and then put AP and AT mines on top of it. It was “6-inch cleared” (relatively safe for personnel) but we were building on top of it, not excavating down.
I think I’ve had a Tomahawk accidentally launched over my head–I don’t know what it was, but I know it was loud and a strange sight to see.
Tripler
In another few months, I’ll have even cooler stuff to tell ya. 
Had sex in the Capital
Monica, is that YOU?
I had the key, briefly, to Strobe pioneer Harold E. “Doc” Edgerton’s darkroom, and used it to develop my strobe photos. And I’ve shared the back seat of a long car ride with Arthur Kantrowitz, founded of Avco Everett Research Labs, the L-5 Society, and other things. (Actually, I’ve had a lot of interaction with him)
Oh, also, forgot to add, just for essoteria: Was playing the part of a pirate in a little interactive-theater thingum (used to be part of an acting troupe), and had to remain as ‘background’ the entire day because my sweat was radioactive; I’d been told no one should come in contact with me. (Our director retroactively named it ‘Radioactive Pirate Day’)
That was in the White House, IIRC.
Well, since hot air balloons aren’t too esoteric, here’s one I bet not many folks here can say: I’ve sat on the Cray-1 (serial number: 1), the first computer Cray ever made. It was sold to Los Alamos National Laboratory back in the 70s, but by the time I got there in 1992, it was too slow and sucked up too much power to justify keeping it running. So, they put it in the lobby of one of the computer center buildings behind the security fence and used it as a bench.
I’ve been within about 50 feet of the space shuttle Challenger.
My husband was Air Force, working public affairs; they were flying the shuttle back across country from a landing at Edwards, and he got called while we were out to dinner with our daughter, whiterabbit, to go escort some bigwig up close and personal. So we got to drive out onto the flight line and go inside the ring of guards and get out and walk around and look at the shuttle sitting there atop the 747.
So technically whiterabbit has done this, too, but she was only about 5 or 6 years old at the time so may not remember it well.