Not people related, but when I was in Vet Medicine, owners would occassionally ask to take home their dog’s testicles after neutering.
Seems normal to me. Going to the hospital for something is a major event for most people. (Children for sure). You bought those postcards and t-shirts when you went to Disneyland and Mexico, right? right? 
When I was 9 or so my brother smacked me on the head with a broom (he was trying to balance it or something - I’d smacked him similarly a few years before. Fair is fair.) necessitating stiches, which the doctor later gave to me. Kept those for a while. Kindof a “Look what I had to have in my head to keep from bleeding all over!” brand of cool. Today it’d have to be titanium screws or something to be really interesting. 
Since we’re talking about teeth, my wife and I have kept the baby teeth of all 3 of our kids. The grandmothers want us to give them one of each, so they can have them made into pendants to wear*. That’s not weird, is it? Hellooooo…, anyone?..
*This is a very Cuban custom, maybe spanish.
My vet gave my former roommate his cat’s testicles after they were removed. The roomie was kidding around, and asked if he could have them after the surgery. The vet, who is a real smartass, saved them and put them in a sample jar. When the roomie went to pick up the cat, the vet just handed him the jar and walked out of the room.
When I had a mole removed from my face last week, I asked the doctor if I could see it after the surgery. They showed it to me (really gross) but then they had to send it off to be tested, so no take home goodies. Oh well.
More animal fun: a wether is a castrated ram (wethers are mostly sold as meat, but sometimes they are kept in the flock as company for the ewes or as part of a ‘spinner’s flock’ like my own), and I recall reading a few years ago about a pair of sheep-raising sisters who were making a fortune selling the dried, wool covered scrotal sacks as cat toys…
I’ll admit, I have one from one of my own sheep, and my cats love it…it just looks like a fluffy cat toy, so it’s fab to tell visitors what it really is…how I got it from this sheep, who is called Demon Baby, is not a story for the faint of heart. But it goes a long way to explaining his personality.
Meanwhile, not only did my mum keep all of my baby teeth, but they’re mixed in with her favourite dog’s…should her jewelry box survive the armageddon, there’s going to be one confused archaeologist down the road…
When I was shot in the face with a BB gun as a kid, my family kept the BB after the surgeons removed it. (I don’t know if we asked for it, though.)
I should ask my parents where it’s stored nowadays…
Oh EEEEEEEEEUUUUUWWW!
Larry, You WIN!!! yucko!!!
I kept my kidney stone for quite some time.
I just didn’t have the heart to get rid of little Joey the Third.
My sister is still pissed that she didn’t get my gallbladder after the surgery. It was apparently huge and chock full of stones and she had planned on giving it a squeeze. She’s so gross.
Say, is she single?
I had my gallbladder removed in '92, using the non-invasive camera style surgery. I can’t remember what they called it, but I can’t pronounce it anyway.
Anyhoo, they took video film of what was happening inside of me during the surgery, and the surgeon asked me if I wanted a copy of it for home viewing.
Errr, no. I don’t want to view my living, pulsating guts, thankyouverymuch.
pugluvr, it’s laparoscopic surgery.
I had my tonsils in a little plastic jar with formaldehyde for a while, until I donated it to my seventh-grade science teacher.
I’ve also got Aaron’s umbilical cord stump, and a sample of the cord blood is kept in San Antonio for possible future use.
Didn’t get to keep the foreskin, though.
Robin
I believe you can keep the placenta and the cord of your baby for medical reasons. Well, the hospital keep those for you!
I have my wisdom teeth! Actually, I think I kept them for a while and threw them away as I really wonder what the purpose was.
I had a piece of bone removed from my ankle and I wanted to see it, but the doctors got rid of it…
Keeping with the Pascal season, please note that several churches in the Middle Ages claimed to have Christ’s foreskin and also Mary’s breastmilk as venerable relics…
Oh, I have a complete video of my knee surgery. Lots of fun at parties.
“What the hell is this video we’re watching?”
“Oh, it’s my knee surgery. See how they had to shave part of the bone off?”
My pediatrician used to keep everything he retrieved from his patients. He would put the object in a little ziploc bag, and put it on a bulletin board in the hallway of his office. Kids put amazing things in their ears, noses, eyes, etc.
I really, really wanted to keep my gallstone. The surgeon said it was one of the biggest stones he’d ever seen, so the greedy bastard kept it for himself.
The doctor that delivered my daughter via C-Section told me that he was retiring and that my daughter was his last baby delivery ever. He came by my hospital room the next day and gave me the towel clamps and two pairs of scissors he’d used during the procedure.
A friend of mine had staples in his legs for quite some time. He got to keep them when they were removed. You can still see some bone fragment on one of them. It’s pretty cool.
This guy is now going through school to become a coroner, so, no surprise that he would want to keep something like that.
I have all four of my wisdom teeth in an envelope. I like looking at them now and then. They’ve still got some dried blood on them.
I heard of a guy who had holes drilled into his and he wore them on a necklace. I thought about doing this, but just never got around to it.
When I was twelve I had to be put under to get four of my teeth (I forget which, but it was prior to my getting braces) out plus my bottom wisdom teeth buds – those were why I was put under, since they had to dig into my jaw after them.
I WANTED to keep my teeth, but they insisted that they HAD to throw them away. My own teeth which had been in my own mouth were too unsanitary for me to take home, or something like that. Idiots.
Good God, I am turning green.
I know of a few WWII guys who have shrapnel that worked it’s way out of their bodies years later, mounted and framed with their Purple Heart medals.
(Ewwwwww, Jebus, the dog really ATE it? :::shiver::: )