What about the other Space Shuttles? Those would be obvious candidates.

They have fewer missions.

I still wonder about piece-parts. The SSME that flew the most missions flew ~20 times. But some laptop, swizzle stick, etc...who knows? Hard to track down.

X-15 have made two flights above the Karman line, Flight 90 at 105.9 km and Flight 91 at 107.8 km, both by Joseph A. Walker. Others are, however, below, with Flight 62 being at 95.9 km so almost.

@DiegoSánchez you can see a spreadsheet showing the missions of all the orbiters here: space.stackexchange.com/a/25415/6944

@DiegoSánchez it's not clear what you mean by "the only one mentioned is Discovery'; the linked evidence shows it is the one with the highest number of flights indeed among the shuttle vehicles.

I wonder if it could be something mundane like the containers they use to ship supplies (food, etc.) to the ISS? I'd assume they get sent back empty (or possibly with waste materials), since they'd just be wasting the limited space up there, and possibly they'd get reused on future resupply missions.

-1I think that by asking "Which particular piece of hardware..." the OP is indeed asking specifically about individual bits, rather than only for entire spacecraft.

@uhoh then, it would be: All the pieces of Discovery hardware that weren't replaced a single time since it's been built (the obvious one I can think of is the internal structural frame). But that might deserve another question.

@LeoS Can that be somehow confirmed that there is indeed no "particular piece of hardware" that was moved from one shuttle to another in order to get it into space more frequently?

If you want to be technically correct on the "replacement parts" certain shuttle tiles flew on all of the flights and were never replaced.

New Shepard has flown 11 times, across three boosters.

@DarrelHoffman Empty containers will go with all the other trash, which is burnt up in the atmosphere - not reused.

I checked on SRB segments but they didn't even get Air Force astronaut wings.

@uhoh you are right, but this is still a good answer

@uhoh, with that narrow interpretation of the question, the technically correct answer would be "The Shuttle Orbiter Discovery's frame, and every piece of hardware mounted to it which hasn't been replaced during the orbiter's lifetime." I think this answer gets that point across well enough, as well as provides supplemental information for anyone with similar questions.

@Ghedipunk I'm thinking about this

@OrganicMarble - Well if you worked for NASA and you don't know, then I think we can rule out there being some intentionally sanctified object that would answer this question. I think the swizzle stick would've 'disappeared' way before 40 w/o there being a paper trail for its provenance, and if there was a trail you would know about it.

@Mazura NASA is(was) vast and I only knew one little corner.

I'm pretty sure all, or almost all Falcon first stages actually make it to space, they just might not until after separation.