Why? I've got 6,000 left.1990? Bryan, it may be time to buy some new corks!
Seriously, about 5 years ago I realized I had the remainder of a bag of 1.75" #9 "premium" corks from 1990. Yeah, 25 years old. When my partner and I closed down our LHBS, a 1,000 count bag of corks was part of my spoils. At that point I had about 1/2 of the bag left, still in the original bag. The corks were dried looking, but solid, and had been stored in my cellar. I had put them aside and literally lost track of them until I was cleaning up old junk.
For the heckuvit I bottled a carboy with them and appeared to have no problems. So I bottled a few more batches, since I already had the corks. I was being economical, right?
For years I had a problem with mold growing on the outside of the corks, a problem produced by my less-than-stellar storage conditions. These corks had that, plus about 10% leaked. Not a huge amount of wine, probably no more than a dozen drops each. Enough to be noticeable. And messy. And irritating.
I gave the remainder of the bag away, and some time after that switched to Nomacorcs, which solved the mold problem.
Surprisingly, I opened the last bottle of those wines at the 3 year mark, and had no quality problems. However, the corks always looked odd when pulled, as the 1/4" next to the wine looked normal, but the remainder of the cork looked dried out.
In hindsight -- bottling more than a few bottles with those ancient corks was risky ("insane" might also be mentioned). These were what was called "premium" at that time, and although labeled #9, they were just a hair larger in diameter than the 1.5" #9's we sold. I suspect that if the corks were the normal ones, a lot more would have leaked.
My opinion on old corks today? If they look dried out, let someone else take the risk.