In the excitement about SpaceX's Falcon recovery and relaunch development program, it's often forgotten in articles like this one that reusable spacecraft were in regular use far back in the 20th century:
SES this week hopes to see its SES-10 communications satellite become the first payload delivered to orbit by a rocket booster that has already completed an orbital launch.
If we specify that "rocket booster" means, precisely, all the parts of the rocket which are involved in providing propellant and thrust at liftoff, then this would seem to be correct.
If we relax our definition a bit to mean something like any airframe with engines which is providing thrust at liftoff, then STS-2 would be the historic flight; Columbia carried a number of scientific experiments on its second orbital mission.
If delivering payload to orbit and leaving it there is a requirement, then some other shuttle flight would qualify.
Since the Shuttle external tanks were not reused, one could argue that none of the shuttle flights qualify, though I consider it disingenuous to consider the ET a dealbreaker while ignoring the Falcon 9 second stage entirely.
That leaves the shuttle SRBs, which could reasonably be argued to be part of "the rocket booster" in a way that the ET is not. The SRBs, however, were also recovered and rebuilt after launch.
Thus, my question is: what was the first shuttle flight in which both the orbiter and the SRB casings were re-used hardware?
For purposes of the question, the SRB wouldn't have to be 100% reused (if, say, nose cones were never reflown) as long as a large majority, say 75% of it was.