The possible places one's soul will go to in the afterlife are:
Souls of mortals go to a place called the Dreamsleeve. There, they are mind-wiped and recycled into a new person - essentially reincarnation, but a bit different.
If you devote yourself to a certain Daedra, though, chances are you'll go to their respective plane of Oblivion instead. Similarly, Nords who follow Shor will go to his plane, Sovngarde.
If you commit to a Daedra, you go to their plane after death.
Redguards go to the Far Shores, just like Nords go to Sovngarde.
From http://www.uesp.net/wiki/Morrowind:Ancestors_and_the_Dunmer :
Spirits that are forced to remain in our world against their will may become mad spirits, or ghosts. Some spirits are bound to this world because of some terrible circumstances of their death, or because of some powerful emotional bond to a person, place, or thing. These are called hauntings.
Some spirits are captured and bound to enchanted items by wizards. If
the binding is involuntary, the spirit usually goes mad. A willing
spirit may or may not retain its sanity, depending on the strength of
the spirit and the wisdom of the enchanter.
Some spirits are bound against their wills to protect family shrines.
This unpleasant fate is reserved for those who have not served the
family faithfully in life. Dutiful and honorable ancestral spirits
often aid in the capture and binding of wayward spirits.
But what happens to a true Nord werewolf who pledged himself to Nocturnal as a Nightingale, but then died valiantly in battle? Who will claim his soul, Shor, Hircine or Nocturnal?