Oblivion:Daedra Heart

The ingredient Daedra Heart is collected from dead Dremora, Xivilai, and (if you have installed Knights of the Nine) Aurorans.

You will need one Daedra Heart to start Boethia's Daedric quest.  If you are suspended from the Mages Guild for murdering a fellow guild member, you will need to collect twenty Daedra Hearts (as well as twenty Vampire Dust) to be reinstated.

Daedra Hearts are nearly identical to Human Hearts.  In particular, the two ingredients share all the same alchemy effects.  Therefore it is particularly easy to make multiple-effect potions using these ingredients (although the only two resulting positive effects are Restore Health and Shock Shield).

Ingredients
There are four guaranteed samples, found in the following locations (magenta crosses on map):
1 sample can be purchased at The Main Ingredient in the Imperial City Market District
1 sample is in the Anvil Fighters Guild Company Offices
1 sample is in the ruins of Ceyatatar
1 sample is in the Embers of Hatred in Random Oblivion World 2, in "The Forbidden" container where Hatreds Soul is found.  Because this Oblivion world can potentially be accessed from multiple Oblivion Gates, this sample can be collected multiple times.
An extra sample is added by the Vile Lair official plug-in. It is located in the bedroom area of Deepscorn Hollow.
It can also be found randomly in the inventories of alchemy vendors (starting at level 12) and in some Conjurer loot chests (starting at level 20).

Creatures
Both Dremora and Xivilai are most commonly encountered in the Planes of Oblivion.  Dremora of various types can be found at any level; Xivilai are usually only found starting at level 22.  The construction set also contains some Daedroths that have Daedra Hearts; however, none of these Daedroths are found in game.

Finding Daedra Hearts in Tamriel is more difficult.  Xivilai can only be found at high levels: at level 22 or higher, they can be found in Conjurer-inhabited ruins (circles on map); at level 25 or higher, they can be found outside Oblivion Gates (squares on map).  Below level 22, Dremora are the only possible source but Dremora are rare in Tamriel.  The few places where Dremora can appear are:
Bravil Wizard's Grotto (red circle) is the only guaranteed place in Tamriel where Dremora can be found.  Two Dremora are located here, a standard Dremora and a boss-level Dremora, both of whom will respawn.  Two Xivilai will also possibly appear here, at level 22 or higher.
Fort Teleman (orange circle) has one boss-level daedric creature (in Fort Teleman Order of the Black Rose) who may be a Dremora at any level, and will respawn.  2 Xivilai are also likely at level 22 or higher.
Brittlerock Cave (purple circle) contains 19 daedric creatures, each of which may possibly be a Dremora at level 5 or higher.
Varondo (purple circle) contains 1-2 daedric creatures, each of which may possibly be a Dremora at level 5 or higher.
Six Oblivion Gates (purple squares) have daedric creatures that may possibly be a Dremora at level 5 or higher.

If you have installed the Knights of the Nine official plug-in, Aurorans provide another source for Daedra Hearts.  Respawning Aurorans can be found in Garlas Malatar, even after the Knights of the Nine questline has been completed.

thumb|left|500 px|Locations of Dremora, Xivilai, and Daedra Hearts