Elder skulls. If you are starting a new character, before you escape Helgen, there is an old Imperial named Torturer in one of the rooms. If you are escaping with the Imperial officer, leave the room with him, then return and kill Torturer and take his skull. The Imperial officer will not attack you when you meet up with him again.

If you've already finished the first quest, Anise is an Elder race woman who lives in a shack by herself, southwest of Riverwood.

Khajiit skulls. Head to Falkreath (south-west of Whiterun) enter the jail and go downstairs. There is a prision cell with Sinding inside. Talk to him to start the Daedric quest "III Met by Moonlight." The quest will bring you to a cave called Bloated Man's Grotto. Inside the cave is a Khajiit named J'Kier. Before he finishes speaking to you, he will die. Take his skull. If you choose to help Sinding defend against the hunters, there will be a few other Khajiit skulls to loot, to boot!

Orc skulls. An Orc skull may also be looted from one of the hunters at Bloated Man's Grotto during the Daedric quest. Once you reach level 10, travel to the Orc stronghold Largashbur, west of Riften. Upon arriving, you will find Orcs fighting a giant, a few of which will likely fall during the battle. You may then loot their skulls.

Vampire skulls. If you don't have the Dawnguard DLC installed and don't want to wait for a random vampire ambush on the road, head to Morthal (north-west of Whiterun). Once there, ask Jarl Idgrod Ravencrone about the burned-down house to start the quest "Laid to Rest." During the quest, you will be able to kill three vampires and loot their skulls--Laelette, Alva and the master vampire Morarth.

Vampire skulls. If your character is at least leven 10, several Vampire skulls may be looted during the Daedric quest "A Daedra's Best Friend." Travel to Falkreath (south-west of Whiterun) and speak to the blacksmith about his lost dog to start the quest.

Breton skulls. A Breton skull may also be looted from the mage Sabastian ♥♥♥♥ during "A Daedra's Best Friend." For more Breton skulls, travel to Markarth (far west of Whiterun) and kill any Forsworn who attack you in the wilderness.

Wood Elf skulls. Faendal is a Wood Elf and potential follower, who lives in Riverwood. Male and female beggars of Skyrim are also Wood Elves. If you kill one while no one is looking you might be able to loot his or her skull. There are a few hunters and fishermen roming the wilderness of Skyrim who are Wood Elves. Corpses of Wood Elves may also be found at:

* Dead Crone Rock, inside a Forsworn tent
* Rannveig's Fast, inside a cage in thre warlock's chamber
* Sunderstone Gorge, near the Word Wall

More info, here:

http://www.uesp.net/wiki/Skyrim:Wood_Elf_%28NPC%29

If you join the Dark Brotherhood, you might receive a quest from Nazir to kill Anoriath, in Whiterun, who is a Wood Elf and brother of Elrindir, who owns the Drunken Huntsman, in Whiterun.

Dremora skulls. After your character reaches level 20, travel to Dawnstar (north of Whiterun) and visit the Dawnstar Museum. Speak to Silus Vesuius, there to start the Daedric quest "Pieces of the Past". The quest ends with a battle against several Dremora. If you survive, you may take their skulls as your prize!

Imperial skulls. If you choose to kill the Imperial Silus Vesuius during the quest, you may take his skull, too. If you join the Stormcloaks, you will have ample opportunity to collect many Imperial skulls during the "Civil War" questline.

Dark Elf skulls. Jenassa, who resides in the Drunken Huntsman in Whiterun, is a Dark Elf, who will become your follower if you pay her 500 gold. Savos Aren is the Arch-Mage at the College of Winterhold (northeast of Whiterun). You may loot his skull after he dies during the "College of Winterhold" questline.

High Elf skulls. The High Elf Ancano also dies during the "College of Winterhold" questline. Bands of Thalmor who roam Skyrim are also High Elves. You may collect several High Elf skulls from Thalmor during the quest "Diplomatic Immunity," which is part of the main questline.

Afflicted skulls. They may be obtained during the Daedric quest "The Only Cure." Travel to the Shrine to Peryite, northeast of Markarth. Speak the the Khajiit Kesh the Clean, there to start the quest.

Nord skulls. There are plenty of bandits who will drop these skulls throughout Skyrim. They are perhaps the easiest to obtain, and not rare at all.

Vampires are also present in Shriekwind Bastion, near Falkreath.

Ender: Thanks for adding to the list. :)