The most famous one is of course from Parashurama - for hiding his kshatriya identity. I also read about a young calf that he kills by mistake and was cursed similarly.
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It is even so, O mighty armed one, as thou sayest, O Bharata! Nothing could resist Karna and Arjuna in battle. This, O sinless one, that I am about to tell thee is unknown to the very gods. Listen to me, O mighty-armed one, as it befell in former days. How all the Kshatriyas, cleansed by weapons should attain to regions of bliss, was the question. For this, a child was conceived by Kunti in her maidenhood, capable of provoking a general war. Endued with great energy, that child came to have the status of a Suta.
The birth of Karna happened because gods wanted to have a divine child capable of provoking a general war.
While thus employed, O Partha, he inadvertently slew, without witting it, the Homa cow of a certain utterer of Brahma who daily performed his Agnihotra rite. Knowing that he had perpetrated that act from inadvertence, he informed the Brahmana of it. Indeed Karna, for the object of gratifying the owner, repeatedly said, 'O holy one, I have killed this thy cow without wilting it. Forgive me the act!' Filled with wrath, the Brahmana, rebuking him, said these words, 'O thou of wicked conduct, thou deservest to be killed. Let the fruit of this act be thine, O thou of wicked soul. While fighting him, O wretch whom thou always challengest, and for whose sake thou strivest so much every day, the earth shall swallow the wheel of thy car! And while the wheel of thy car shall thus be swallowed up by the earth, thy foe, putting forth his prowess, will cut off thy head, thyself being stupefied the while! Leave me, O vile man! As thou hast heedlessly slain this my cow, even so wilt thy foe cut off thy head while thou shalt be heedless!'
1st curse of Karna from Brahmana
One day Rama of great intelligence, while roving with Karna in the vicinity or his retreat, felt very weak in consequence of the fasts he had undergone. From affection begotten by confidence, the tired son of Jamadagni placing his head on Karna's lap, slept soundly, White his preceptor was thus sleeping (with head) on his lap, a frightful worm, whose bite was very painful and which subsisted on phlegm and fat and flesh and blood, approached the presence of Karna. That blood-sucking worm, approaching Karna's thigh, began to pierce it. Through fear of (awaking) his preceptor, Karna became unable to either throw away or kill that worm. Though his limb was bored through by that worm, O Bharata, the son of Surya, lest his preceptor should awake, suffered it to do its pleasure. Though the pain was intolerable, Karna bore it with heroic patience, and continued to hold Bhrigu's son on his lap, without quivering in the least and without manifesting any sign of pain. When at last Karna's blood touched the body of Rama of great energy, the latter awoke and said these words in fear, 'Alas, I have been made impure! What is this that thou art doing, Tell me, casting off all fear, what is the truth of this matter!' Then Karna informed him of that worm's bite
Then Rama wrathfully addressed Karna, saying, 'O fool, no Brahmana could endure such agony. Thy patience is like that of a Kshatriya. Tell me the truth, without fear.' Thus asked, Karna, fearing to be cursed, and seeking to gratify him, said these words, 'O thou of Bhrigu's race, know me for a Suta, a race that has sprung from the intermixture of Brahmanas with Kshatriyas. People call me Karna the son of Radha. O thou of Bhrigu's race, be gratified with my poor self that has acted from the desire of obtaining weapons. There is no doubt in this that a reverend preceptor in the Vedas and other branches of knowledge is one's father. It was for this that I introduced myself to thee as a person of thy own race.' Unto the cheerless and trembling Karna, prostrated with joined hands upon earth, that foremost one of Bhrigu's race, smiling though filled with wrath, answered, 'Since thou hast, from avarice of weapons, behaved here with falsehood, therefore, O wretch, this Brahma weapon shalt not dwell in thy remembrance.
Karna was bitten by the bug and Karna told he was no Brahmin so Parshuram cursed him that he will not remember the Brahma weapon when he needs it the most.
Narada also tells Yudhisthira various reasons that caused the death of Karna
When, for thy good, the Lord of the celestials begged of him his (natural) coat of mail and ear-rings, stupefied by celestial illusion, he gave away those precious possessions. Deprived of his car-rings and divested of his natural armour, he was slain by Arjuna in Vasudeva's presence. In consequence of a Brahmana's curse, as also of the curse of the illustrious Rama, of the boon granted to Kunti and the illusion practised on him by Indra, of his depreciation by Bhishma as only half a car-warrior, at the tale of Rathas and Atirathas, of the destruction of his energy caused by Salya (with his keen speeches), of Vasudeva's policy, and, lastly of the celestial weapons obtained by Arjuna from Rudra and Indra and Yama and Varuna and Kuvera and Drona and the illustrious Kripa, the wielder of Gandiva succeeded in slaying Vikartana's son Karna of effulgence like that of Surya himself. Even thus had thy brother been cursed and beguiled by many."
These are many reasons how Arjuna succeeded in slaying Karna.