Did Karna ever spare Arjuna's life in Kurushetra? Or he only spared other four pandavas' lives but never Arjun?
Karna spared other 4 pandava's lives because he had promised Maata Kunti that "your 5 sons will be alive".
5)either Karna or Arjun
(remember that Karna was the eldest son of Maata Kunti with blessings from the Sun God -- Surya).
He gave "jeevan daan" to 4 (let the 4 go and did not kill them.)
"Mahabharata" Anushasan parwa.
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Karna didn't spare the life of Arjuna on 16th day and this myth has arised from B.R Chopra's version of Mahabharata continued in Ramanand Sagar's Krishna and then in many internet articles and blogs but according to authentic Sanskrit Mahabharata it was Arjuna who won on 16th day and made Karna helpless to save Kauravas from getting defeated by Pandavas. Here's the reference from Mahabharata Critical Edition published in Sanskrit and translated in English by Bibek Debroy :-
कर्ण पर्व, अध्याय क्र.21, श्लोक क्र.31-श्लोक क्र.42
31 अथ कर्णास्त्रम अस्त्रेण परतिहत्यार्जुनः सवयम दिशः खं चैव भूमिं च परावृणॊच छरवृष्टिभिः
32 मुसलानीव निष्पेतुः परिघा इव चेषवः शतघ्न्य इव चाप्य अन्ये वज्राण्य उग्राणि वापरे
33 तैर वध्यमानं तत सैन्यं सपत्त्यश्वरथद्विपम निमीलिताक्षम अत्यर्थम उदभ्राम्यत समन्ततः
34 निष्कैवल्यं तदा युद्धं परापुर अश्वनरद्विपाः वध्यमानाः शरैर अन्ये तदा भीताः परदुद्रुवुः
35 एवं तेषां तदा युद्धे संसक्तानां जयैषिणाम गिरिमस्तं समासाद्य परत्यपद्यत भानुमान
36 तमसा च महाराज रजसा च विशेषतः न किं चित परत्यपश्याम शुभं वा यदि वाशुभम
37 ते तरसन्तॊ महेष्वासा रात्रियुद्धस्य भारत अपयानं ततश चक्रुः सहिताः सर्ववाजिभिः
38 कौरवेषु च यातेषु तदा राजन दिनक्षये जयं सुमनसः पराप्य पार्थाः सवशिबिरं ययुः
39 वादित्रशब्दैर विविधैः सिंहनादैश च नर्तितैः परान अवहसन्तश च सतुवन्तश चाच्युतार्जुनौ
40 कृते ऽवहारे तैर वीरैः सैनिकाः सर्व एव ते आशिषः पाण्डवेयेषु परायुज्यन्त नरेश्वराः
41 ततः कृते ऽवहारे च परहृष्टाः कुरुपाण्डवाः निशायां शिबिरं गत्वा नयविशन्त नरेश्वराः
42 यक्षरक्षःपिशाचाश च शवापदानि च संघशः जग्मुर आयॊधनं घॊरं रुद्रस्यानर्तनॊपमम
Karna Parva, Section No. 21, Shloka No. 31 - Shloka No. 42
Then, Arjuna himself countered Karna’s weapons with his own weapons. He enveloped the directions, the sky and the earth with his showers of arrows. Those arrows descended like clubs and bludgeons. Some were like shataghnis and others were as fierce as the vajra. The soldiers, the foot soldiers, horses, rathas and elephants, were destroyed. They closed their eyes, uttered woes of lamentation and fled distractedly in different directions. In that battle, horses, men and elephants were destroyed. The soldiers were killed by the arrows and terrified, fled. ‘ “Thus did they engage in battle, desiring victory. The sun approached Mount Asta. 278 O great king! In particular, there was darkness and dust. We could not see anything, favourable or unfavourable. O descendant of the Bharata lineage! The great archers were frightened of fighting in the night. With all their horses, they therefore withdrew. 279 O king! When the Kouravas departed at the end of the day, the Parthas were delighted in their minds at having obtained victory and also left for their own camps. They showed contempt for the enemy by sounding many kinds of musical instruments, roaring like lions, dancing and praising Achyuta and Arjuna. When the brave ones and all the soldiers retreated, all the lords of men pronounced benedictions on the Pandaveyas. Having retreated, the Kurus and the Pandavas were cheerful. The lords of men went to their camps in the night and rested. Large numbers of yakshas, rakshas, pishachas and carnivorous beasts went to that terrible field of battle, which was like Rudra’s dancing arena.” ’
So as everyone can read nowhere it's mentioned that Karna defeated Arjuna on 16th day and spared him. On the contrary it's clearly written that Pandavas defeated Kauravas after Arjuna countered the weapons of Karna.