Lots of things are used in the making of wands, Dragon Heartstrings, unicorn hairs, phoenix feathers, however some much more interesting and expanded lore could be derived from the use of other things in wands, like Basilisk scales, Bogart... Goo?, or some physical essence of dementor. I know that Fleur Delacour's wand uses Veela hair, and accord to this question/answer it is purely Olivander's choice to limit himself to the three primary core types. Is there any canon example of other parts being used to make a wand, and if so, is there an exhaustive list of magical components used?
For example, President Seraphina Picquery had a wand made by Violetta Beauvais, and thus containing a core of rougarou hair. From Pottermore:
Violetta Beauvais, the famous wandmaker of New Orleans, refused for many years to divulge the secret core of her wands, which were always made of swamp mayhaw wood. Eventually it was discovered that they contained hair of the rougarou, the dangerous dog-headed monster that prowled Louisiana swamps. It was often said of Beauvais wands that they took to Dark magic like vampires to blood, yet many an American wizarding hero of the 1920s went into battle armed only with a Beauvais wand, and President Picquery herself was known to possess one.
There were also wandmakers hailing from the United States who used a variety of cores in their wands, such as the feathers of a thunderbird, the spines of the White River Monster, or the hair of a wampus cat.
Even in Europe, where Ollivander dominated, there were many other possible wand cores. The Elder Wand, for example, posssesses a core of thestral hair.:
I decided that the core of the Elder Wand is the tail hair of a Thestral; a powerful and tricky substance that can be mastered only by a witch or wizard capable of facing death.
And of course, before Ollivander started using only the three Supreme Cores, a wide variety of materials were used in wands:
Early in my career, as I watched my wandmaker father wrestling with substandard wand core materials such as kelpie hair, I conceived the ambition to discover the finest cores and to work only with those when my time came to take over the family business.
As an example, the wand of Sir Cadogan is believed to have had a core of troll whisker.
Blackthorn and troll whisker, nine inches, combustible.
The wand of Salazar Slytherin contained a piece of the horn of a basilisk, almost certainly the self-same beast he hid in the Chamber of Secrets:
In all the years that she had lived with it, Isolt had never known that she held in her hand the wand of Salazar Slytherin, one of the founders of Hogwarts, and that it contained a fragment of a magical snake’s horn: in this case, a Basilisk.