(Note: this is a collection of the meanings attributed to the cards by some occultists in the past centuries. It does not reflect my own study or opinion of the cards. It is only meant as a quick comparative reference as I develop my own take.)

Paul Foster Case (and Ann Davies)

When well aspected the powers listed above are expressed by a personality represented by the King of Wands. However these same qualities when overly strong or intense can express as cruelty, oppression, ostentation and pride. Thus in Tarot divination, besides the basic principles expressed by Ab, the Father, and Yod, the Creative principle, the King of Wands has these specific meanings:
Well Dignified: an ardent, impulsive, influential man; one possessed of authority and strongly marked by the quality of leadership; somewhat hasty in temper but just, generous and friendly. lll Dignified: the same general type but cruel, ill-natured, intolerant and probably unfriendly to the querent.
(From the Oracle of Tarot course)

A. E. Waite

The physical and emotional nature to which this card is attributed is dark, ardent, lithe, animated, impassioned, noble. The King uplifts a flowering wand, and wears, like his three correspondences in the remaining suits, what is called a cap of maintenance beneath his crown. He connects with the symbol of the lion, which is emblazoned on the back of his throne. Divinatory Meanings: Dark man, friendly, countryman, generally married, honest and conscientious. The card always signifies honesty, and may mean news concerning an unexpected heritage to fall in before very long. Reversed: Good, but severe; austere, yet tolerant.
(From The Pictorial Key to the Tarot)

Aleister Crowley

(Note: Crowley and the Golden Dawn swap around King and Knight. This is in part true of Waite as well.)
The Knight of Wands represents the fiery part of Fire; he rules from the 21St degree of Scorpio to the 20th degree of Sagittarius. He is a warrior in complete armour. On his helmet for a crest he wears a black horse. In his hand he bears a flaming torch; a flame also in his mantle; and upon the flames does he ride. His steed is a black horse leaping.

The moral qualities appropriate to this figure are activity, generosity, fierceness, impetuosity, pride, impulsiveness, swiftness in unpredictable actions. If wrongly energized, he is evil-minded, cruel, bigoted and brutal. He is in either case ill-fitted to carry on his action; he has no means of modifying it according to circumstances. If he fails in his first effort, he has no resource.

In the Yi King, the fiery part of Fire is represented by the 51st hexagram, Kan. The signification there given is entirely in accordance with the doctrine of the Tarot, but great emphasis is laid on the startling, perilous, and revolutionary character of the events cognate. The Querent is advised to be apprehensive, yet cool, resolute and energetic: to beware of untimely action, but to go forward with tense confidence in his own ability.

All these correspondences of the Yi King are to be studied in that book (S.B.E. vol. XVI) and reference is here made to the text when important passages are too long to be conveniently quoted.
(From the Book of Thoth)

Golden Dawn’s Book T

A KINGLY Figure with a golden, winged crown, seated on a chariot. He has large white wings. One wheel of his chariot is shewn. He wears corslet and buskins of scale armour decorated with a winged lion’s head, which symbol also surmounts his crown. His chariot is drawn by a lion. His arms are bare, save for the shoulder-pieces of the corslet, and he bears a torch or fire-wand, somewhat similar to that of the Zelator Adeptus Minor. Beneath the chariot are flames, some waved, some salient.
Swift, strong, hasty; rather violent, yet just and generous; noble and scorning meanness.
If ill dignified — cruel, intolerant, prejudiced and ill natured.

Etteilla

Country man
Upright. This card, as far as the medicine of the spirit is concerned, means, in its natural position: Country Man, Good and Stern Man, Well Intentioned Man, Honest Man. – Conscience, Probity. – Farmer, Worker, Cultivator.
Reversed. Good and stern man – Indulgence, Severity, Forbearance, Condescension.