Temurah Chapter 7, Mishnah 4. In the previous Mishnah we learned that a consecrated animal that died must be buried, and from here the Mishnah goes on to list additional items that require burial. According to the Bartenura and most commentators, everything listed here is forbidden to derive benefit from, and since there is no way to make any use of them, the Sages required that they be buried - after all, what else can be done with them? Since this is a rabbinic requirement, there is a certain flexibility regarding other alternatives. The Rambam, however, apparently understood that the obligation of burial is a law given to Moshe at Sinai.
"V'eilu hen hanikbarin":
"Kodashim shehipilu - yikavru" - Consecrated animals that miscarried must be buried. An animal that was consecrated, for example a ewe consecrated as a shelamim offering, which miscarried its young. The miscarried fetus, which is dead, has the same status as its mother and is therefore consecrated, yet it is not fit to be offered. And just as a consecrated animal that died requires burial, so too the miscarried fetus requires burial.
"Hipilah shilya - tikaver" - The same applies when no actual fetus was found but only a placenta was expelled. The placenta is the sac in which the fetus develops, and the Sages had a principle that there is no placenta without a fetus - a sac does not develop in the mother's womb unless a fetus grew in it. Even though we do not know what became of the fetus (it may have dissolved), the placenta requires burial.
"Shor hanniskal" - An ox whose verdict of death was rendered, and likewise any animal that killed a person and underwent a formal trial in which it was confirmed that it indeed killed him. In the Mishnah as cited in the Gemara there is even a case of a rooster that pecked a baby's head and the baby died. The carcass of the animal after it is put to death is forbidden to derive benefit from and requires burial.
"V'eglah arufah" - As you will recall from the parashah, when a corpse is found in the Land of Israel and it is not known how it got there or who killed the person, the elders of the nearest city go out, bring a calf to a nachal eisan (a stream bed that is not plowed), break its neck there, wash their hands there and declare that they bear no responsibility for the death of the murdered man. That calf whose neck was broken is forbidden to derive benefit from and requires burial.
"V'tzipporei metzora" - A metzora who has been healed undergoes a multi-stage purification process. In the first stage two free birds are taken; one of them is slaughtered and its blood is received in a vessel containing spring water, and this mixture is sprinkled on the metzora by means of dipping the second, living bird in it, after which the living bird is sent away free outside the city. The bird that was slaughtered is forbidden to derive benefit from and requires burial. And although the Mishnah used the plural, "birds of a metzora," it does not mean the two birds of the process - for the bird that is sent away, if it is later caught, is not forbidden to derive benefit from - but rather all the birds slaughtered for the purification of metzoraim.
"U'sear nazir" - The nazir accepts upon himself to abstain from grape products, not to become tamei to a corpse, and to shave his hair at the conclusion of his nezirus. Upon completing his nezirus he shaves all his hair, and the shaved hair is thrown into the fire beneath the pot in which his shelamim are cooking and is burned there. But if he became tamei with corpse tumah in the middle of the process and must start over, that procedure too includes shaving - and there is no pot and no shelamim, since he did not complete his nezirus successfully. This shaved hair is forbidden to derive benefit from and must be buried in the ground.
"U'peter chamor" - The firstborn male donkey. As we learned in Maseches Bechoros, a donkey that has a male firstborn opening of the womb must be redeemed with a sheep, a goat or a lamb. And if the owner is unwilling to redeem it, the donkey's neck must be broken, and it is forbidden to derive benefit from it. This is what the first opinion derives from the gezeirah shavah of "arifah" and "arifah," which links the eglah arufah to the peter chamor, and according to this view it is forbidden to derive benefit from it until it is redeemed, and as long as it is not redeemed it remains in its prohibited state. The bottom line: the donkey whose neck was broken requires burial, and one may not derive benefit from it.
"U'basar b'chalav":
The wording is worth clarifying: many think that these are two words, "basar" and, with the conjunctive vav, "v'chalav," and this is not correct. The text reads "basar b'chalav" with a beis - meat in milk. Three times the Torah says "Lo sevashel gedi ba'chalev imo" - do not cook a kid, meaning a young goat, in its mother's milk - and the Sages derived that the three statements come to teach three separate prohibitions:
The prohibition of the cooking itself - even without eating at all, the very act of cooking them together is forbidden.
The prohibition of eating - meat and milk that were cooked together may not be eaten.
The prohibition of benefit - one may not derive any economic benefit from them. For example, one may not feed them to a dog, since doing so saves money on buying dog food, and it turns out that he benefits from them.
What, then, can be done with meat and milk that were cooked together? A clarification is in order: when the meat and milk were not cooked together, the prohibition is only rabbinic - for example, a sandwich with a slice of roast beef and a slice of cheese between two slices of bread, where one who eats it transgresses a rabbinic prohibition. But if they were cooked together in an oven, the prohibition is from the Torah, and at that point the prohibition of benefit and the obligation to bury them apply. The Rema brings all of this at the end of the laws of meat and milk (chapter 19), and quotes this Mishnah almost word for word. In the Shulchan Aruch I did not find a place where it states that meat and milk require burial, and therefore it is not certain whether this is required at all; as far as I know it is only forbidden to derive benefit from it.
"V'chullin shenishchatu ba'azarah":
A non-consecrated animal that was slaughtered inside the Beis HaMikdash is forbidden to derive benefit from and requires burial. It is obvious that a person who brings in a cow and slaughters it in the Mikdash falls into this prohibition, but it can also happen to someone who came to the Mikdash to slaughter properly: he slaughtered the animal, and they ask him - what was this? Did you designate it in advance as an olah? And he answers that he did not. Since he did not designate it in advance as an olah, it is not an olah, for it must be designated beforehand; and so this is an example of slaughtering non-consecrated animals in the azarah - a negative prohibition, and the meat is forbidden to derive benefit from.
The view of Rabbi Shimon:
"Rabbi Shimon omer: chullin shenishchatu ba'azarah - yisarfu" - Rabbi Shimon says: non-consecrated animals slaughtered in the azarah must be burned. Rabbi Shimon too agrees that strictly speaking there is nothing here beyond a general prohibition of benefit, and burning is not required, except that in his view an obvious confusion is liable to arise from this: those who see a person bring an animal, slaughter it, and then see it disqualified and buried, are liable to think that an offering that became disqualified in the Mikdash is to be buried and not burned. Whereas the halachah is that a disqualified offering requires burning in a special place, the beis hasereifah, and not merely burial. Because of the concern for this error, Rabbi Shimon holds that any non-consecrated animal slaughtered in the Mikdash requires burning and not burial. And the halachah does not follow him.
The Mishnah continues: "V'chen chayah shenishchatah ba'azarah" - and likewise a wild animal that was slaughtered in the azarah. According to Rabbi Shimon, not only does a cow, goat or sheep that was not consecrated as an offering and was slaughtered in the azarah require rabbinic burning, but even something further removed - a wild animal, such as a deer. It is clear to everyone that a deer is not fit to be an offering, and slaughtering it in the azarah is nothing but non-consecrated slaughter in the Mikdash; and nevertheless, out of concern that onlookers will err and think that a disqualified offering is to be buried and not burned, when in fact the requirement is burning, Rabbi Shimon requires burning for all non-consecrated animals slaughtered in the azarah. And again - the halachah does not follow Rabbi Shimon.