(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)

The Three of Cups is astrologically related to the second decanate of Cancer ruled by the Scorpio aspect of Mars, time period July 2 to July 12. The distinct meanings in divination combine the pleasure and emotion associated with the suit of Cups and the sex magnetism of the Scorpio aspect of Mars, together with Cancerian practicality and penchant for attachments.
Well-Dignified: activity, determination, practicality; fondness for pleasure and comfort; attachments and attractions to the opposite sex; pleasure, merriment, eating and drinking, plenty of new clothes, etc.
Ill-Dignified: danger of the ‘triangle’ situation; trouble through attachments to the opposite sex; midunderstandings; prodigality; sensuality.
Keyword: Enjoyment
(From the Oracle of Tarot course)

A. E. Waite

Maidens in a garden-ground with cups uplifted, as if pledging one another. Divinatory Meanings: The conclusion of any matter in plenty, perfection and merriment; happy issue, victory, fulfilment, solace, healing, Reversed: Expedition, dispatch, achievement, end. It signifies also the side of excess in physical enjoyment, and the pleasures of the senses.
(From The Pictorial Key to the Tarot)

Aleister Crowley

The Three of Cups is called the Lord of Abundance. The idea of love has come to fruition; but this is now sufficiently far down the Tree to introduce a very definite differentiation between the suits, which was not previously possible.

[…]

This card refers to Binah in the suit of Water. This is the card of Demeter or Persephone. The Cups are pomegranates: they are filled bountifully to overflowing from a single lotus, arising from the dark calm sea characteristic of Binah. There is here the fulifilment of the Will of Love in abounding joy. It is the spiritual basis of fertility.

The card is referred to the influence of Mercury in Cancer; this carries further the above thesis. Mercury is the Will or Word of the All-Father; here its influence descends upon the most receptive of the Signs.

At the same time, the combination of these forms of energy brings in the possibility of somewhat mysterious ideas. Binah, the Great Sea, is the Moon in one aspect, but Saturn in another; and Mercury, besides being the Word or Will of the All-One, is the guide of the souls of the Dead. This card requires great subtlety of interpretation. The pomegranate was the fruit which Persephone ate in the realms of Pluto, thereby enabling him to hold her in the lower world, even after the most powerful influence had been brought to bear. The lesson seems to be that the good things of life, although enjoyed, should be distrusted.
(From The Book of Thoth)

Golden Dawn’s Book T

A WHITE Radiating Hand, as before, holds a group of lotuses or water-lilies, from which two flowers rise on either side of, and overhanging the top cup; pouring into it the white water. Flowers in the same way pour white water into the lower cups. All the cups overflow; the topmost into the two others, and these upon the lower part of the card. Cups are arranged in an erect equilateral triangle. Mercury and Cancer above and below.
Abundance, plenty, success, pleasure, sensuality, passive success, good luck and fortune; love, gladness, kindness, liberality.
Binah of HB:H (Plenty, hospitality, eating and drinking, pleasure, dancing, new clothes, merriment).

Etteilla

Success
Upright. This card, as far as the medicine of the spirit is concerned, means, in its natural position: Success, Science, Happy outcome, Happy solution, Victory. – Healing, Cure, Relief. – Accomplishment. – Perfection.
Reversed. Dispatch, Sending, Execution, Completion, End, Conclusion, Termination, Fulfillment.

MQS