Karna is widely known as Daana Veera Karna. What are the incidents from the Mahabharata that establish this?
This question talks about a lot of other qualities Karna had.
In Mahabharata, Vana Parva, it is mentioned that if someone ask for anything after bathing and Sun-worship, Karna will not refuse this.
And when, O foremost of monarchs, Karna after rising from the water, used at mid-day to worship the effulgent Surya with joined hands, the Brahmanas used to solicit him for wealth. And at that time there was nothing that he would not give away to the twice-born ones.
When the illustrious slayer of Paka refused to ask for any other boon, Kama with a smile again addressed him, saying, 'O god of gods, even before this, I had recognised thee, O Lord! O Sakra, it is not proper for me to confer on thee any unprofitable boon, for thou art the very lord of the celestials! On the contrary, being as thou art the Creator and lord of all beings, it is thou that shouldst confer boons on me! If, O god, I give thee this coat of mail and ear-rings, then I am sure to meet with destruction, and thou shalt also undergo ridicule! Therefore, O Sakra, take my earrings and excellent mail in exchange for something conferred by thee on me! Otherwise, I will not bestow them on thee!'
Other incident which proves Karna as Daan Veera is when Kunti has asked him to join Pandavas side in battle, Karna had refused it but promised that he will not kill Yudhishthira, Bhima, Nakula and Sahadeva. He has said to Kunti that, "Your five sons will be alive by the end of the war. Either I will die or Arjuna". And in the war Karna has fulfilled that wish of Kunti.
Except Arjuna, thy other sons, Yudhishthira, Bhima, and the twins, though capable of being withstood by me in tight and capable also of being slain, shall not yet be slain by me. It is with Arjuna alone, among all the combatants of Yudhishthira, that I will fight. Slaying Arjuna in battle, I shall achieve great merit, or slain by Savyasachin, I shall be covered with glory. O famous lady, the number of thy sons will never be less than five. Five it will always be,--either with me, or with Arjuna, and myself slain.'