What are all the curses given by sage Durvasa?
If possible list all such curses and also the persons to whom the curses were given.
I know of four stories in Hindu scripture involving Durvasa cursing or threatening to curse someone:
This chapter of the Vishnu Purana describes how Durvasa gave Indra a garland, and Indra's elephant Airavatam threw it on the ground. So Durvasa cursed Indra and the gods to lose their powers, which is what necessitated the famous Churning of the Ocean to obtain Amrita:
Durvásas, a portion of Śankara (Śiva), was wandering over the earth; when be beheld, in the hands of a nymph of air, a garland of flowers culled from the trees of heaven, the fragrant odour of which spread throughout the forest, and enraptured all who dwelt beneath its shade. The sage, who was then possessed by religious phrensy, when he beheld that garland, demanded it of the graceful and full-eyed nymph, who, bowing to him reverentially, immediately presented it to him. He, as one frantic, placed the chaplet upon his brow, and thus decorated resumed his path; when he beheld (Indra) the husband of Śachí, the ruler of the three worlds, approach, seated on his infuriated elephant Airávata, and attended by the gods. The phrensied sage, taking from his head the garland of flowers, amidst which the bees collected ambrosia, threw it to the king of the gods, who caught it, and suspended it on the brow of Airávata, where it shone like the river Jáhnaví, glittering on the dark summit of the mountain Kailása. The elephant, whose eyes were dim with inebriety, and attracted by the smell, took hold of the garland with his trunk, and cast it on the earth. That chief of sages, Durvásas, was highly incensed at this disrespectful treatment of his gift, and thus angrily addressed the sovereign of the immortals: "Inflated with the intoxication of power, Vásava, vile of spirit, thou art an idiot not to respect the garland I presented to thee, which was the dwelling of Fortune (Śrí). Thou hast not acknowledged it as a largess; thou hast not bowed thyself before me; thou hast not placed the wreath upon thy head, with thy countenance expanding with delight. Now, fool, for that thou hast not infinitely prized the garland that I gave thee, thy sovereignty over the three worlds shall be subverted. Thou confoundest me, Śakra, with other Brahmans, and hence I have suffered disrespect from thy arrogance: but in like manner as thou hast cast the garland I gave thee down on the ground, so shall thy dominion over the universe be whelmed in ruin. Thou hast offended one whose wrath is dreaded by all created things, king of the gods, even me, by thine excessive pride."
Descending hastily from his elephant, Mahendra endeavoured to appease the sinless Durvásas: but to the excuses and prostrations of the thousand-eyed, the Muni answered, "I am not of a compassionate heart, nor is forgiveness congenial to my nature. Other Munis may relent; but know me, Śakra, to be Durvásas. Thou hast in vain been rendered insolent by Gautama and others; for know me, Indra, to be Durvásas, whose nature is a stranger to remorse. Thou hast been flattered by Vaśisht́ha and other tender-hearted saints, whose loud praises (lave made thee so arrogant, that thou hast insulted me. But who is there in the universe that can behold my countenance, dark with frowns, and surrounded by my blazing hair, and not tremble? What need of words? I will not forgive, whatever semblance of humility thou mayest assume."
This chapter of the Srimad Bhagavatam describes how Ambarisha was engaging in an Ekadasi fast in honor of Vishnu here, and Durvasa came to him, asking for food. Then Durvasa went to take a bath, and Ambarisha had some water before Durvasa came back because it was important to break the fast at the right time. Durvasa was furious, and created a demon to kill Ambarisha, but then Vishnu destroyed the demon with his Sudarshana Chakra, which began to chase Durvasa until he fell at Ambarisha's feet:
After giving these cows, the King first sumptuously fed all the brāhmaṇas, and when they were fully satisfied, he was about to observe the end of Ekādaśī, with their permission, by breaking the fast. Exactly at that time, however, Durvāsā Muni, the great and powerful mystic, appeared on the scene as an uninvited guest. After standing up to receive Durvāsā Muni, King Ambarīṣa offered him a seat and paraphernalia of worship. Then, sitting at his feet, the King requested the great sage to eat. Durvāsā Muni gladly accepted the request of Mahārāja Ambarīṣa, but to perform the regulative ritualistic ceremonies he went to the river Yamunā. There he dipped into the water of the auspicious Yamunā and meditated upon the impersonal Brahman. In the meantime, only a muhūrta of the Dvādaśī day was left on which to break the fast. Consequently, it was imperative that the fast be broken immediately. In this dangerous situation, the King consulted learned brāhmaṇas. The King said: “To transgress the laws of respectful behavior toward the brāhmaṇas is certainly a great offense. On the other hand, if one does not observe the breaking of the fast within the time of Dvādaśī, there is a flaw in one’s observance of the vow. Therefore, O brāhmaṇas, if you think that it will be auspicious and not irreligious, I shall break the fast by drinking water.” In this way, after consulting with the brāhmaṇas, the King reached this decision, for according to brahminical opinion, drinking water may be accepted as eating and also as not eating. O best of the Kuru dynasty, after he drank some water, King Ambarīṣa, meditating upon the Supreme Personality of Godhead within his heart, waited for the return of the great mystic Durvāsā Muni. After executing the ritualistic ceremonies to be performed at noon, Durvāsā returned from the bank of the Yamunā. The King received him well, offering all respects, but Durvāsā Muni, by his mystic power, could understand that King Ambarīṣa had drunk water without his permission. Still hungry, Durvāsā Muni, his body trembling, his face curved and his eyebrows crooked in a frown, angrily spoke as follows to King Ambarīṣa, who stood before him with folded hands. "Alas, just see the behavior of this cruel man! He is not a devotee of Lord Viṣṇu. Being proud of his material opulence and his position, he considers himself God. Just see how he has transgressed the laws of religion. Mahārāja Ambarīṣa, you have invited me to eat as a guest, but instead of feeding me, you yourself have eaten first. Because of your misbehavior, I shall show you something to punish you." As Durvāsā Muni said this, his face became red with anger.
Uprooting a bunch of hair from his head, he created a demon resembling the blazing fire of devastation to punish Mahārāja Ambarīṣa. Taking a trident in his hand and making the surface of the earth tremble with his footsteps, that blazing creature came before Mahārāja Ambarīṣa. But the King, upon seeing him, was not at all disturbed and did not move even slightly from his position. As fire in the forest immediately burns to ashes an angry snake, so, by the previous order of the Supreme Personality of Godhead, His disc, the Sudarśana cakra, immediately burnt to ashes the created demon to protect the Lord’s devotee. Upon seeing that his own attempt had failed and that the Sudarśana cakra was moving toward him, Durvāsā Muni became very frightened and began to run in all directions to save his life.
This chapter of the Uttara Kanda of the Ramayana describes how when Rama was meeting with Yama and Lakshmana was standing guard, Durvasa threatened to curse all of Ayodhya unless Lakshmana let him see Rama immediately. To avoid the curse Lakshmana interrupted Rama's meeting, which ultimately led to Rama being forced to disown Lakshmana:
While Rama and Kala were thus conversing with one another, the great ascetic Durvasa arrived at the gate for seeing Rama and approaching Lakshmana said: O Saumitri, do thou soon take me to Rama; my time goes away, so do thou take me first." Hearing the words of the ascetic, Lakshmana, the slayer of enemies worshipping the feet of that high souled one, said "O illustrious Sir, kindly mention thy business. What is thy object ?Order me what I am to do. Rama is engaged in some business so kindly wait here for some time." Hearing those words that foremost of Rishis, Durvasa, impatient with rage, said with blood red eyes: O Saumitri, if dost thou not go even this very moment and communicate unto Rama my arrival, I shall impricate thee, Rama, Bharata, Satrughna, your sons and grand sons. I shall curse also thy kingdom and cities. I cannot any longer restrain my growing fire." Hearing those dreadful and resolute words of the Rishi, Lakshmana thought within himself: My own destruction is far more desirable than that of all." Having thus resolved Lakshmana approached Rama and communicated unto him the intelligence. Heaing the words of Lakshmana and having bade adieu, unto Kala, Rama soon came out and saw Atri s son. And having saluted that great and powerful ascetic he with folded hands, said "What is thine business." Hearing the words of Rama, the highly powerful Durvasa, the foremost of Munis, said. "Hear, O Rama fond of virtue. For a thousand years I have carried on the vow of fasting. It has terminated to day, so do thou give me food as much as possible." Hearing those words Rama was greatly delighted and gave proper food unto that ascetic. And feasting on that nectar like sweet food, Durvasa, the foremost of Rishis, thanked Rama and repaired to his own hermitage. Thereupon remembering the words of Kala, Rama was greatly sorry.
This excerpt from the Vasudeva Mahatmya describes an incarnation of Vishnu who will be born in the Kali Yuga accompanied by sages who will be born as ordinary humans due to "the curse of Munis":
When the Asuras killed by me as Krishna and by Arjuna in the battles, will promote and establish Adharma (unrighteous practices) on the earth, I, sage Narayana, shall be born on the earth from my devotee Dharmadeva in the land of Koshala, as a Brahmana singer of Saman hymns. O Aja (Brahma), establishing the boly Dharma I shall be the protector of sages who will be born as men by the curse of Munis (other sages) as well as Uddhava, O child.
As I discuss in this question, followers of Swaminarayan believe that this prophecy is about him, and they also believe that the Munis mentioned include Durvasa.
Now there are some additional stories of Durvasa cursing people which do not have a basis in Hindu scripture. There's the famous story of Dushyanta losing his memories of Shakuntala due to a curse of Durvasa, for instance. Also, the Vana Parva of the Mahabharata describes how Duryodhana brought Durvasa to the Pandavas in an attempt to get Durvasa to get angry and curse the Pandavas, but Durvasa was never angered in the first place due to Krishna's intervention.