I buried my Whitey cat in the backyard of the house where we lived at the time. We moved about a year later and I seriously considered bringing Whitey with us, but decided he should stay in a place he knew. I would like to be able to visit him, but as an atheist, I also feel that he could not be “visited” in any case.
Heh. I didn’t even know you could donate a pet’s body to science - makes sense, though. I’d probably do that, when the time comes. 
This is the first time I’ve come across that option, too, Mr. Excellent. I think it’s because the place where she died is a whizzy, critical care/specialist veterinary hospital. Our dog had an somewhat unusual, usually fatal chronic condition and if her body could add anything to their knowledge of this crappy disease, then we were all for it.
Several months after one of my dogs died, a tiny bird’s nest got blown out of one of our trees after a storm. It had JC’s hair woven into it. I still have that nest.
Most buried at home, a few cremated and kept. A small collection buried at my uncle’s.
I have to admit, though—after many years, and a good many animals (many of whom came old or sick), burial considerations went from “there’s a nice spot on the hill, where the sun shines through the trees in the morning” to “aw, crap…where do we still have room?” My appeals to dig one deep shaft with a removable slab that we could progressively fill in went mostly unheeded.
Plus, it wasn’t so much “soil” we (read: I) had to dig it as much as “a close weave of roots and rocks, designed to hold redwood silt in place.”
I’ve also cremated a few rats in a wood-burning stove. My suggestions that this could be easily adapted to—well, you get what I’m saying. No luck.
I used a combination of the above for my cat a couple of years ago. I had him cremated, and they gave me back his ashes in a sealed wood box. He was always a sun-seeker, so I found a place in the back yard that gets a lot of sun, and buried his ashes there.
I went for that, but it was the ‘other place’ part I was voting for, not the pet cemetary. We don’t have a garden, so we buried our pet rat on a field at the nearby city farm. My daughter and her best friend read out poems and everything and made a nice little headstone.
Her name was Poppy and, by coincidence, there are now poppies growing on her grave.
One of the many reasons for us getting pets was so that my daughter would kinda learn how to cope with death of a loved one, so burying her was essential. I don’t think she’d have learned much beneficial if we’d thrown Poppy out with the rubbish.
For the several cats I’ve lost over the years, I’ve chosen in all but one case to leave the body for disposal with the vet’s office; when the spirit departs, what’s left is only a shell. I grieve as I say goodbye, staying with them throughout the release; I grieve afterwards in the emptiness their loss leaves behind. One cat’s body I did take home with me and bury near the home I then lived in; in less than two years, though, I moved from there, and have no access to visit the grave again.
I have only had to put down one horse – so far; with two aging geldings, I know some day I will face this again. Fortunately, where I keep them now, it will be possible to bury them at the edge of the farm’s hayfields, to lie next to two of the owners’ late horses. Another boarder has the heavy equipment that has been and will be needed to dig the hole and do the burial.
I would plan (so far as one can plan this sort of thing) to be with my horse for the euthanasia, then leave before the actual burial. That is what I did when my beloved Nick died. He was spending the summer at a friend’s farm in New Hampshire when he was injured and had to be put down. He was buried in a field where he had loved to graze. I chose the spot because I have a picture of him grazing there.
Crockett (collie) and Buffy (golden retriever) were cremated (individual ashes) and buried in my parents’ back yard. Fergus (collie) was cremated and is sitting on the entertainment center in a wooden box at my dad’s. It’s kind of joke now (I wanted to bury him last time I was home which was met with disapproval) and he still gets his Christmas stocking hung under his wooden box.