They decided to take out my appendix when I had infant umbilical hernia surgery.
That was it until a few years ago I had a parotidectomy and partial neck dissection that took 30 something lymph nodes and most of my right parotid gland. My face is even more lopsided now.
Uninstalled:
I still have all 3 of my wisdom teeth (the 4th never came in). My dentist is jonesing for removal of one of them, tho, so he can better work on a developing cavity in the next tooth forward.
Tonsils still there. Congenital hernia repair at age 5 or 6.
Otherwise, all is still there and functional, I presume.
Tonsils & some teeth gone.
In chronological order:
tonsils and adenoids
corneas
uterus, fallopian tubes, one ovary
appendix
some breast tissue (cancer)
and 7 or 8 biopsies
Plus wisdom teeth, though I thought the OP said not to include those.
No uterus as of last fall, but I do still have my appendix and tonsils, and I have some extra hardware in one of my knees.
No surgeries, but I have had permanent teeth removed as part of orthodonture.
It may be hard to believe by those who know me here, but I have a small mouth.
Sans a couple of teeth and a gallbladder…
Do you mind me asking what made them decide to take your wisdom teeth so late? I have all four of mine still. Or maybe I should say “now” instead - the first three came in during my 20s per usual, but the 4th one that a dentist told me would never erupt began to finally come in right before my 37th birthday. That was a surprise.
I’ve lost my foreskin, tonsils and adenoids, teeth, moles, appendix, and as of two months ago, my right knee joint.
Apart from the disposable parts, skin cells, nails, etc. I’m entirely whole, with the exception of my foreskin. Even have my wisdom teeth.
Foreskin, as a baby
Appendix, age 10
Tonsils, age 11
Rotten tooth pulled, age 17
Wisdom teeth, age 30+
But never a broken bone (yet!)
Missing:
Foreskin
Appendix
2 out of 4 wisdom teeth (both top)
Partially original:
I had root canals in high school on both of my lower front teeth so they are missing some of the original parts. They also became more susceptible to wear and cracking and had to be rebuilt with unoriginal bits in my early 40s.
This could become known as " The Winter Of Our Missing Contents " !!!
hmmmm. I also had some teeth out before I got braces. I was also told that I had a “small jaw”. I later read/saw a report that this type of thing wasn’t necessarily done for legitimate reasons/because it was really necessary, that it was a “scam” to make money. I’ve felt annoyed about it ever since… 
Besides the usual, I’m short two C-spine disks.
The only original hardware that I’m missing is my left ACL. The had to jury-rig a strip of a tendon in its place when I went in for repairs.
I had some teeth out before getting braces back in the early 1970s. But I wonder if things changed as science marched on over the last 40+ years.
I recently went to a new dentist. He wanted to know my dental history, so I told him, including the fact that I wore braces way back when, and the fact that some of my teeth were pulled before getting braces. He said, yes, that was common in those days, but orthodontia has come a long way since then; and nowadays, every effort is made to work with the teeth that were formerly in the way.
I’m inclined to believe my dentist, but I’ll allow that there may have been a chance that there was some money-making going on. Either way, I doubt we’ll ever know for sure. My feeling is that it was so long ago, and my father’s insurance covered it anyway, that it doesn’t concern me now.
Why is everyone mentioning teeth?
The OP excluded teeth from the scope.
Teeth are a big loss. Sometimes as in wisdom teeth it’s a very traumatic thing. Baby teeth, yea every one goes through that. Not everyone has adult teeth extracted. Just saying.
You’re correct, and it is a good question. Perhaps we should chew on it for a while. 
(Sorry, it needed to be said.)