Through his mother he was a grandson of George II of England (like William V of Orange). A sister of his mother was married to King Fredrick V of Denmark. Karl married a daughter of theirs and had a number of children by her. Interestingly William IV of Orange was through his mother grandson of an earlier Charles Landgrave of Hesse-Kassel.
His sons seem to have died without reproducing.. His oldest daughter married King Fredrick VI of Denmark. But it was the son of Karl's youngest daughter who later became King Christian IX of Denmark.
Christian IX had a number of children. Fredrick VIII from whom the current Queen of Denmark descends, and other Scandinavian Royalty as well. And a daughter Alexandra who became Queen-Consort of England and an ancestor of Elizabeth II.
But most interesting to me is that King George I of Greece was a son of King Christian IX of Denmark. George I is the direct Pater-lineal Ancestor of the current King in Exile of Greece who is named Constantine, and his children including the Crown Prince. The oldest son of the Crown-Prince is also named Constantine, Prince Constantine-Alexios. But the oldest child of the Crown-Prince is a daughter, Princess Marie-Olympia who's now doing magazine cover shoots like she was a Hollywood celebrity or something (I don't think Karl of Hesse-Kassel is the ancestor she gets her looks from).
But through a different son George I of Greece is the direct Pater-lineal ancestor of the husband of Queen Elizabeth. Making him the paternal progenitor of Prince Charles, William and Harry.
Greece and Denmark having the same Royal Family makes me think of Ezekiel 27 referring to Dan and Javan being linked to each other. And that same family slowly becoming the British Royal Family can be interesting since I believe Tarshish was ancient Britain of Solomon's time. And that family descending from a documented Illuminati member and leader of German Freemasonry at the time of the French Revolution is pretty interesting.
Fredrick V of Denmark's ancestry can be traced back through Duchess Marie Elisabeth of Saxony to Anne of Bohemia and Hungry. Anne was the daughter of Vladislaus II. Through the Kings of Bohemia her ancestry can be traced back to Wenceslaus I of Bohemia, who was the son of Constance of Hungry, who was the daughter of Agnes of Antioch who was the daughter of Constance of Antioch who was the daughter of Alice of Antioch.
Alice was one of the daughters of Baldwin II of Jerusalem and Morphia of Melitene. The later of whom's ancestry I discus here.
Update: September 11th 2015.
The direct Pater-lineal Ancestry of Karl of Hesse-Kassel can be traced back to Henry I Langrave of Hesse.
Henry was through his mother's mother also a descendant of Anges of Antioch through her son Andrew II of Hungry. Through his mother he was heir to the Landgraves of Thuringia.
Through his father Henry II Duke of Barbant he was among other things potential heir to Stephen I of England and Matlida of Blounge daughter of Eustace III of Boulonge brother of Godfrey de Boulonge and Baldwin I of Jerusalem.
Descent from Matilda is the nearest line of descent possible from the original royal family of Crusader Jerusalem. Everyone formally claiming the title King of Jerusalem today does so from Baldwin II, who's claim to even being a cousin of them seems unverifiable.
Stephen I of England was a grandson of William The Conqueror through his mother. Through his father he was a descendant of Louis IV of France and Kings of Burgundy.
The direct pater-lineal ancestry of Eustace, Godfrey and Baldwin went back to Baldwin II of Flanders, son of Baldwin I of Flanders and Judith daughter of Charles The Bald, a successor of Charlemagne. He was also a descendant of Louis IV. Baldwin I of Flanders seems to be a count already when he shows up in history, it's possible he already had Merovingian ancestry, but we don't know for sure.
In the line from Henry I to Karl is Louise I of Hesse, father of Henry III of Hesse, who's daughter Elisabeth of Hesse married John V of Nassau. Their son was William I Count of Nassau, who was the father of William I of Orange aka William The Silent. He had a number of children by a number of wives, one of them was Countess Louise Juliana of Nassau, great grandmother of King George I of England. William the Silent was also the direct pater-lineal ancestor of William III who became King of England in the Glorious Revolution of 1688. He is the central figure behind the mythology of the Orange Order and the The Orange Lodge.
The Pater-lineal ancestor of King George I of England was Frederick IV Elector Palatine. His mother was another Elisabeth of Hesse, daughter of Philip I Landgrave of Hesse. Another son of her's was Charles IX of Sweden.
And of course the direct Successor of William of Orange was Queen Julliana of the Netherlands, who's husband Prince Bernhard of the Netherlands was one of the original founders of the Bilderberg group. They were the parents of Queen Beatrix. Also of the Royal Family of the Netherland was Prince Frederich son of King William Frederick I who was Grand Master of Dutch Freemasonry for much of the 19th Century.
I've talked about the two Dukes of Brunswick during Karl's time before, who Nesta Webster confused with each other. The paternal common ancestor of both was Ferdinand Albert II Duke of Brunswick. Through his mother he descended from Maurice Landgrave of Hesse-Kassel. And the younger Duke is an ancestor of Princess Helena of Nassau and thus of Queen Juliana.
Christian of Hesse-Dramstadt is also a known Illuminati Member inducted in 1783. The house of Hesse-Dramstadt shares the house of Hesse-Kassel's descent from Henry I of Hesse. Likewise Frederickt V of Hesse-Hormburg. Another Illuminatus, Karl August von Sachsen-Wiemar-Eisenach, married Louise daughter of Louis IX of Hesse-Dramstadt (Christian's Sister). From that marriage descended among other people Helene Duchess of Orleans and thus the current heir to the Orleanist Bourbon Crown. And Charles Alexander who married Princess Sophie of the Netherlands. Another brother to Christian was Louise X of Hesse-Dramstadt who was a known member of Amis Reunis Lodge of Paris which became allied with the Illuminati due to the efforts of Bode.
Going back to Frederick V of Denmark. His paternal grandfather Frederick IV of Denmark was the son of Christian V by Charlotte Amaile of Hesse-Kassael, the daughter of William VI Langrave of Hesse-Kassel. And she was actually his first born offspring, but standards of the time always favored oldest male over an older woman to be successor.
Update: September 20th 2015
The second wife of Philippe I Duke of Orleans and mother of his successor Philippe II was Elizabeth Charlotte of the Pallatine, daughter of Charles I Louis Elector Palatine and Charlotte of Hesse-Kassel. daughter of William V Langrave of Hesse-Kassel. The Orelanist house having a genealogical connection to Hesse-Kassel is very interesting. Charles I Louise himself has descent from both Elisabeth of Hesse and William The Silent.
The daughter of Philippe I of Orelans and Charlotte of Pallatine was Elisabeth Charlotte d'Orleans. Who was the mother of Prince Charles Alexander de Lorraine. Who was one of the alleged Grand Masters of the Prior of Sion in Plantard's hoax. Likewise she was the grandmother of the next alleged Grand Master Maxamillian de Lorraine. I mention only because I suspect that obvious hoax drew on many real conspiracies.
The Hesse-Kassel family can be shown to have a connection to the occult already well before Karl. Maurice The Learned (also a direct of ancestor of Charlotte) is an interesting figure, to copy/paste from Terry Melanson's Illuminati Conpsiracey Part One.
The Hesse-Kassel family may well be the key to connecting a lot of esoteric mysteries.
Also if the theory about the Count of Saint-Germain being the son of Francis II of Transylvania is true, then his mother was of the house of Hesse also. Which is interesting since at the end of his life Saint-Germain lived on Karl's estate. Amusingly Francis II himself was descended from a Zsofia Bathori.
Update 2/26/2016: Barbarossa
The mother of King George I of England was Sophia Countess of Palatine Simmern. She descends from Philip the Magnanimous Landgrave of Hesse, one of the pater-lineal ancestors of Karl of Hesse-Kassel. He descends from Anne of Saxony daughter of Frederick I Elector of Saxony.
Frederick of Saxony descends on his mother's side from Henry I Landgrave of Hesse. But his direct pater-lineal ancestry was from Frederick I Margrave of Meissen. Frederick of Meissen's mother's pater-lineal descent was from Frederick Barbarossa an important Holy Roman Emperor.
Barbarossa was a descendant of Baldwin IV of Flanders making him a part of one of the most interesting to me lines of descent from Charlemagne and Alfred The Great. He was also buried in Antioch and has become subject of King in The Mountain type legends, giving him important esoteric significance.