At least Buddy leaves them in the litter box! I can count on tootsie rolls from The Black Cat (she has a name, but we don’t use it, for some reason) in front of the box most days. Yes, she has been checked out by the vet. It seems to be a territory thing. Feliway spray doesn’t help, nor does having boxes in two different parts of the basement. We just live with it.
My cat does this too. I’ve seen her pulling socks out through the holes in the laundry basket and carrying them gently downstairs. I hate to stop her. She looks so purposeful.
Oh, man. Hahahah!! “Tootsie Rolls”. I am cracking up really hard at that. 
Hey, maybe you should call her Tootsie.
The still living gifts are more memorable than the dead ones. Besides lots of mice, my cats have provided me with live specimens of a chipmunk, a couple of birds, and a decent sized frog. I have no idea where the frog came from. There are no bodies of water nearby.
Not once has any cat I’ve had actually eaten the thing they killed…
I’m seeing quite a lot of cat stories, but very few dog ones. And they say cats are the more civilzed pet. 
I don’t think dogs bring ‘gifts’ really, my dog finds things and brings them to the house, but I’m pretty sure they’re just for him.
My cat brings me pieces of elastic from my sewing room, and cries piteously while she does it. I have no idea why.
He must’ve thought you were really hungry.
My wife now makes sure to zip up or otherwise close her purse when she puts it down, due to the generosity of our fearless (indoor) huntress, Smoke. Reaching into her purse one morning, looking for her phone, she drew pack her hand quickly because she felt a bug on it. As it turns out, Smoke had left her a present of a small, white, perfectly intact moth.
A couple months after I got my old dog Bitz the Wondermutt I started finding dead doves and grackles in the back yard. I didn’t put 2 and 2 together for a while and couldn’t understand why the was a dead bird around every week or two. Perfectly intact, but dead as charity.
One day I was sitting on the patio reading. Bitz was lying in the sun about 10 feet away. A dove landed about 4 feet in front of her. She collected her feet under her, crept forward, barked and lunged. The bark startled the bird and Bitz caught it in her mouth as she completed the lunge. Then she shook the thing vigorously, trotted over to me all proud and dropped it at my feet, sopping wet but completely unmarked.
She got a couple good sized chunks of steak for both putting on such an impressive show and being so generous with her bounty. Gods, I miss that dog.
I once owned a cat who brought a rabbit into the house for me. Unfortunately, the rabbit was still alive and proceeded to tear around the house once inside and free of the cat. Then I finally caught the thing and took it to a wildlife shelter but they told me it was unsavable and would have to be destroyed.
Thanks, cat!
Though I was impressed that he could manhandle a live, full-grown rabbit and drag it up onto the deck and keep it in check while he meowed at me to let him in with it.
I used to know a couple who had a smallish orange and white dog. It was an Austrailian something. Not Shepherd because those are black and white. About the same size though. They lived out in the country with a lot of woods around their property. The dog dragged home entire deer corpses on a regular basis. Often enough for them to be pretty sure he was killing them himself, even though they were way bigger than him. The dog would get a hind leg and lots of praise as a reward, and the rest would go into stew.
Gifts my pets have left me:
dead rabbits
live baby rabbits to take away from them
dead squirrels
dead birds
live birds (ohmygod)
dead mice
moles (and mole asses!)
dead possums
dead armadillos
live raccoon which had to be killed by my husband
Best of all is when my cats have left me the “choicest parts” of a big ol’ rat or mouse–the liver, heart, etc, in a glistening pile on the front step or (yuck) the entertainment center.
(Oh, and the inevitable poops, pees, hairballs, pukes and such.)
Everything bigger/meaner than the rabbit in my list above was from my dog(s), who are VERY protective of THEIR property.
This cat has taken sock-stealing to new heights:-
http://news.bbc.co.uk/1/hi/england/leicestershire/8030168.stm
My dog once brought home a large turtle shell. I have no idea where he found it, but I am pretty sure the turtle was long gone by the time he did. It wasn’t for us though. He loved carrying that thing around, like a shield or something.
Oh and I just remembered, when I was a kid, our dog DJ used to steal laundry that people had hanging from clotheslines. My mom would hang them up on the telephpne pole in front of our house, and they were usually reclaimed…
When Bitz and I would go camping I’d let her range at night.
One morning I woke up, came out of the tent and next to the tent she had neatly piled three cow vertebrae, four ribs and part of the skull. Apparently she found an interesting pile of bones while on her evening rounds.
A bedroom full of feathers and a dead bird on my door. I also use my cats to catch any insects that show up in my bathroom. I live in brazil and I am terrified of bugs.
An hour or so before we were to show our house to prospective buyers, I discovered a good-sized garter snake sunning itself under the grow lights in the basement room I used to start seedlings. I had no idea how a snake would have gotten in. A few days later, I found a baby garter snake in the dining room. Hmmm. Maybe the one in the basement was the mommy.
A day or two after that, I caught one of my indoor-only cats coming back into the house through a small hole in the screen on the porch with a live snake in her mouth. Mystery solved.
We lived in Africa for three years. I lost count of the number of dead geckos. She never ate them, just killed them and left them outside our bedroom door.